a sprinter accelerates from 1.40 m/s to 9.00 m/s in 1.10s. what is her acceleration in m/s2?
iii Motion Along a Straight Line
3 Chapter Review
Key Terms
- acceleration due to gravity
- acceleration of an object as a result of gravity
- average acceleration
- the rate of alter in velocity; the alter in velocity over time
- average speed
- the full altitude traveled divided by elapsed fourth dimension
- average velocity
- the displacement divided by the time over which displacement occurs
- displacement
- the alter in position of an object
- distance traveled
- the total length of the path traveled betwixt two positions
- elapsed fourth dimension
- the departure between the catastrophe time and the start time
- free fall
- the state of move that results from gravitational force only
- instantaneous acceleration
- acceleration at a specific point in time
- instantaneous speed
- the absolute value of the instantaneous velocity
- instantaneous velocity
- the velocity at a specific instant or time betoken
- kinematics
- the description of motility through backdrop such as position, time, velocity, and acceleration
- position
- the location of an object at a particular time
- total deportation
- the sum of individual displacements over a given time menstruation
- two-body pursuit problem
- a kinematics problem in which the unknowns are calculated by solving the kinematic equations simultaneously for two moving objects
Cardinal Equations
| Displacement | Δ x = x f − 10 i Δx=xf−xi |
| Total displacement | Δ x Total = ∑ Δ x i ΔxTotal=∑ Δxi |
| Boilerplate velocity | five – = Δ ten Δ t = ten two − ten 1 t 2 − t 1 five–=ΔxΔt=x2−x1t2−t1 |
| Instantaneous velocity | v ( t ) = d x ( t ) d t v(t)=dx(t)dt |
| Average speed | Average speed = south – = Total distance Elapsed time Average speed=s–=Total distanceElapsed time |
| Instantaneous speed | Instantaneous speed = ∣∣ five ( t ) ∣∣ Instantaneous speed=|5(t)| |
| Average acceleration | a – = Δ 5 Δ t = v f − v 0 t f − t 0 a–=ΔvΔt=vf−v0tf−t0 |
| Instantaneous acceleration | a ( t ) = d v ( t ) d t a(t)=dv(t)dt |
| Position from boilerplate velocity | x = ten 0 + v – t x=x0+5–t |
| Boilerplate velocity | 5 – = v 0 + 5 2 v–=v0+v2 |
| Velocity from acceleration | 5 = v 0 + a t ( constant a ) v=v0+at(constanta) |
| Position from velocity and acceleration | x = x 0 + 5 0 t + 1 2 a t 2 ( constant a ) ten=x0+v0t+12at2(constanta) |
| Velocity from distance | v 2 = v 2 0 + 2 a ( 10 − x 0 ) ( constant a ) v2=v02+2a(10−x0)(constanta) |
| Velocity of free fall | v = five 0 − g t (positive upward) v=v0−gt(positive upward) |
| Height of free fall | y = y 0 + v 0 t − 1 two g t 2 y=y0+v0t−12gt2 |
| Velocity of free autumn from height | v ii = v 2 0 − two g ( y − y 0 ) v2=v02−2g(y−y0) |
| Velocity from acceleration | v ( t ) = ∫ a ( t ) d t + C ane v(t)=∫a(t)dt+C1 |
| Position from velocity | x ( t ) = ∫ v ( t ) d t + C 2 x(t)=∫v(t)dt+C2 |
Summary
3.one Position, Deportation, and Average Velocity
- Kinematics is the description of motion without considering its causes. In this chapter, information technology is express to motility along a direct line, called one-dimensional motion.
- Deportation is the alter in position of an object. The SI unit for displacement is the meter. Displacement has direction as well as magnitude.
- Distance traveled is the total length of the path traveled between two positions.
- Fourth dimension is measured in terms of change. The time between 2 position points x 1 x1 and x 2 x2 is Δ t = t 2 − t one Δt=t2−t1 . Elapsed time for an upshot is Δ t = t f − t 0 Δt=tf−t0 , where t f tf is the final time and t 0 t0 is the initial time. The initial time is often taken to be naught.
- Boilerplate velocity v – v– is divers equally displacement divided past elapsed time. If x ane , t ane x1,t1 and x 2 , t ii x2,t2 are ii position time points, the average velocity between these points is
v – = Δ 10 Δ t = 10 2 − 10 ane t two − t ane . 5–=ΔxΔt=x2−x1t2−t1.
3.2 Instantaneous Velocity and Speed
- Instantaneous velocity is a continuous function of time and gives the velocity at whatever indicate in time during a particle's motion. Nosotros can calculate the instantaneous velocity at a specific time by taking the derivative of the position function, which gives usa the functional course of instantaneous velocityv(t).
- Instantaneous velocity is a vector and tin can exist negative.
- Instantaneous speed is plant by taking the accented value of instantaneous velocity, and it is e'er positive.
- Average speed is full distance traveled divided by elapsed time.
- The gradient of a position-versus-time graph at a specific time gives instantaneous velocity at that time.
3.iii Average and Instantaneous Acceleration
- Acceleration is the rate at which velocity changes. Acceleration is a vector; information technology has both a magnitude and direction. The SI unit for acceleration is meters per second squared.
- Acceleration can be caused by a change in the magnitude or the direction of the velocity, or both.
- Instantaneous accelerationa(t) is a continuous office of time and gives the acceleration at any specific time during the motion. Information technology is calculated from the derivative of the velocity function. Instantaneous acceleration is the slope of the velocity-versus-time graph.
- Negative acceleration (sometimes called deceleration) is acceleration in the negative management in the called coordinate system.
three.four Motion with Constant Acceleration
- When analyzing one-dimensional motion with constant acceleration, identify the known quantities and choose the appropriate equations to solve for the unknowns. Either 1 or 2 of the kinematic equations are needed to solve for the unknowns, depending on the known and unknown quantities.
- Two-body pursuit problems always require ii equations to exist solved simultaneously for the unknowns.
3.five Free Fall
- An object in gratis autumn experiences constant dispatch if air resistance is negligible.
- On World, all free-falling objects have an dispatchone thousand due to gravity, which averages g = nine.81 m/s 2 1000=9.81m/s2 .
- For objects in gratuitous fall, the up direction is unremarkably taken as positive for displacement, velocity, and acceleration.
3.6 Finding Velocity and Displacement from Acceleration
- Integral calculus gives us a more complete conception of kinematics.
- If dispatcha(t) is known, we can use integral calculus to derive expressions for velocityv(t) and positionx(t).
- If acceleration is constant, the integral equations reduce to Equation three.12 and Equation 3.13 for move with constant dispatch.
Conceptual Questions
3.one Position, Displacement, and Average Velocity
1.
Requite an example in which there are clear distinctions amid altitude traveled, deportation, and magnitude of displacement. Place each quantity in your example specifically.
ii .
Nether what circumstances does altitude traveled equal magnitude of displacement? What is the just case in which magnitude of deportation and displacement are exactly the same?
3.
Bacteria move dorsum and forth using their flagella (structures that look similar little tails). Speeds of up to 50 μm/s (50 × 10−61000/southward) have been observed. The total distance traveled past a bacterium is big for its size, whereas its displacement is small. Why is this?
4 .
Give an example of a device used to measure time and place what change in that device indicates a change in time.
5.
Does a car's odometer measure distance traveled or displacement?
6 .
During a given time interval the average velocity of an object is zippo. What can you say conclude about its deportation over the time interval?
3.2 Instantaneous Velocity and Speed
7.
There is a distinction between average speed and the magnitude of average velocity. Give an case that illustrates the departure between these two quantities.
eight .
Does the speedometer of a motorcar measure out speed or velocity?
9.
If y'all divide the full altitude traveled on a car trip (as determined by the odometer) by the elapsed fourth dimension of the trip, are you calculating average speed or magnitude of average velocity? Nether what circumstances are these ii quantities the same?
10 .
How are instantaneous velocity and instantaneous speed related to one another? How practice they differ?
3.3 Boilerplate and Instantaneous Dispatch
11.
Is it possible for speed to be constant while dispatch is non zero?
12 .
Is it possible for velocity to exist constant while acceleration is not aught? Explain.
thirteen.
Give an case in which velocity is null yet acceleration is non.
14 .
If a subway train is moving to the left (has a negative velocity) and so comes to a stop, what is the direction of its dispatch? Is the acceleration positive or negative?
15.
Plus and minus signs are used in i-dimensional motility to bespeak management. What is the sign of an dispatch that reduces the magnitude of a negative velocity? Of a positive velocity?
three.4 Motion with Constant Acceleration
sixteen .
When analyzing the motility of a single object, what is the required number of known physical variables that are needed to solve for the unknown quantities using the kinematic equations?
17.
State two scenarios of the kinematics of single object where three known quantities crave two kinematic equations to solve for the unknowns.
3.5 Free Fall
18 .
What is the acceleration of a rock thrown straight upward on the way upwards? At the top of its flight? On the way down? Assume at that place is no air resistance.
19.
An object that is thrown directly up falls back to Globe. This is one-dimensional motion. (a) When is its velocity zero? (b) Does its velocity alter direction? (c) Does the acceleration accept the same sign on the fashion up as on the style downward?
20 .
Suppose you throw a rock most straight up at a coconut in a palm tree and the rock just misses the kokosnoot on the way up but hits the coconut on the way down. Neglecting air resistance and the slight horizontal variation in motion to account for the striking and miss of the coconut, how does the speed of the rock when information technology hits the coconut on the manner down compare with what it would have been if it had hit the coconut on the way upward? Is it more than likely to dislodge the kokosnoot on the way up or downward? Explain.
21.
The severity of a fall depends on your speed when y'all strike the ground. All factors simply the dispatch from gravity being the same, how many times higher could a rubber fall on the Moon than on Globe (gravitational acceleration on the Moon is most one-sixth that of the World)?
22 .
How many times college could an astronaut bound on the Moon than on World if her takeoff speed is the same in both locations (gravitational acceleration on the Moon is about on-sixth of that on Earth)?
three.6 Finding Velocity and Displacement from Acceleration
23 .
When given the acceleration function, what additional data is needed to find the velocity part and position function?
Issues
3.1 Position, Displacement, and Average Velocity
24 .
Consider a coordinate system in which the positivex axis is directed upward vertically. What are the positions of a particle (a) 5.0 m directly above the origin and (b) ii.0 m below the origin?
25.
A car is 2.0 km west of a traffic lite att = 0 and 5.0 km east of the light att = 6.0 min. Assume the origin of the coordinate arrangement is the light and the positiveten direction is eastward. (a) What are the machine'south position vectors at these ii times? (b) What is the car'southward displacement between 0 min and half-dozen.0 min?
26 .
The Shanghai maglev train connects Longyang Road to Pudong International Aerodrome, a altitude of thirty km. The journeying takes 8 minutes on average. What is the maglev train'due south average velocity?
27.
The position of a particle moving along thex-centrality is given by x ( t ) = four.0 − ii.0 t x(t)=4.0−2.0t m. (a) At what time does the particle cross the origin? (b) What is the displacement of the particle betwixt t = iii.0 s t=3.0s and t = six.0 s ? t=half dozen.0s?
28 .
A cyclist rides eight.0 km due east for twenty minutes, then he turns and heads west for 8 minutes and 3.ii km. Finally, he rides e for 16 km, which takes 40 minutes. (a) What is the final displacement of the cyclist? (b) What is his average velocity?
29.
On Feb 15, 2013, a superbolide shooting star (brighter than the Sun) entered Earth's atmosphere over Chelyabinsk, Russia, and exploded at an altitude of 23.5 km. Eyewitnesses could feel the intense heat from the fireball, and the blast wave from the explosion blew out windows in buildings. The nail wave took approximately 2 minutes thirty seconds to reach footing level. (a) What was the average velocity of the nail wave? b) Compare this with the speed of sound, which is 343 m/s at sea level.
3.2 Instantaneous Velocity and Speed
30 .
A woodchuck runs 20 m to the right in 5 southward, then turns and runs ten yard to the left in three s. (a) What is the average velocity of the woodchuck? (b) What is its average speed?
31.
Sketch the velocity-versus-time graph from the following position-versus-time graph.
32 .
Sketch the velocity-versus-time graph from the following position-versus-time graph.
33.
Given the following velocity-versus-time graph, sketch the position-versus-time graph.
34 .
An object has a position functionx(t) = 5t m. (a) What is the velocity as a function of time? (b) Graph the position function and the velocity function.
35.
A particle moves along theten-axis according to x ( t ) = 10 t − 2 t ii m 10(t)=10t−2t2m . (a) What is the instantaneous velocity att = ii s andt = 3 s? (b) What is the instantaneous speed at these times? (c) What is the average velocity betweent = 2 southward andt = three s?
36 .
Unreasonable results. A particle moves along thex-axis co-ordinate to ten ( t ) = 3 t 3 + 5 t x(t)=3t3+5t . At what time is the velocity of the particle equal to zero? Is this reasonable?
3.iii Average and Instantaneous Dispatch
37.
A cheetah tin accelerate from rest to a speed of 30.0 m/south in vii.00 s. What is its acceleration?
38 .
Dr. John Paul Stapp was a U.South. Air Force officeholder who studied the effects of extreme acceleration on the homo torso. On December 10, 1954, Stapp rode a rocket sled, accelerating from residuum to a peak speed of 282 m/s (1015 km/h) in v.00 s and was brought jarringly back to rest in only ane.twoscore s. Calculate his (a) acceleration in his management of motion and (b) acceleration contrary to his direction of motion. Express each in multiples ofg (nine.80 m/sii) past taking its ratio to the acceleration of gravity.
39.
Sketch the acceleration-versus-fourth dimension graph from the post-obit velocity-versus-time graph.
40 .
A commuter backs her car out of her garage with an acceleration of 1.40 m/due south2. (a) How long does it take her to reach a speed of 2.00 m/south? (b) If she then brakes to a stop in 0.800 s, what is her acceleration?
41.
Assume an intercontinental ballistic missile goes from remainder to a suborbital speed of half dozen.50 km/south in lx.0 s (the actual speed and fourth dimension are classified). What is its average acceleration in meters per 2d and in multiples ofm (9.fourscore m/s2)?
42 .
An airplane, starting from rest, moves down the runway at constant acceleration for 18 s and then takes off at a speed of threescore yard/s. What is the average acceleration of the airplane?
3.4 Motion with Constant Acceleration
43.
A particle moves in a straight line at a constant velocity of 30 grand/southward. What is its deportation between t = 0 and t = 5.0 s?
44 .
A particle moves in a straight line with an initial velocity of 30 m/due south and a constant acceleration of xxx m/due south2. If at t = 0 , x = 0 t=0,10=0 and v = 0 5=0 , what is the particle's position att = 5 due south?
45.
A particle moves in a straight line with an initial velocity of thirty 1000/s and abiding acceleration 30 m/southward2. (a) What is its displacement att = 5 s? (b) What is its velocity at this same time?
46 .
(a) Sketch a graph of velocity versus time corresponding to the graph of displacement versus time given in the post-obit figure. (b) Identify the time or times (t a,t b,t c, etc.) at which the instantaneous velocity has the greatest positive value. (c) At which times is it zero? (d) At which times is it negative?
47.
(a) Sketch a graph of dispatch versus time respective to the graph of velocity versus time given in the following effigy. (b) Identify the time or times (t a,t b,t c, etc.) at which the dispatch has the greatest positive value. (c) At which times is it zero? (d) At which times is it negative?
48 .
A particle has a constant acceleration of 6.0 grand/s2. (a) If its initial velocity is ii.0 chiliad/s, at what time is its displacement 5.0 m? (b) What is its velocity at that fourth dimension?
49.
Att = 10 south, a particle is moving from left to right with a speed of v.0 m/south. Att = 20 s, the particle is moving right to left with a speed of 8.0 m/due south. Bold the particle's acceleration is abiding, determine (a) its acceleration, (b) its initial velocity, and (c) the instant when its velocity is zero.
fifty .
A well-thrown ball is caught in a well-padded mitt. If the dispatch of the brawl is 2.ten × ten 4 m/south 2 2.10×104m/s2 , and 1.85 ms ( ane ms = x −3 due south ) (1ms=10−3s) elapses from the time the brawl first touches the paw until it stops, what is the initial velocity of the brawl?
51.
A bullet in a gun is accelerated from the firing bedroom to the finish of the barrel at an average rate of half dozen.20 × 10 5 m/southward 2 vi.20×105m/s2 for 8.ten × x − four due south 8.10×10−4s . What is its muzzle velocity (that is, its final velocity)?
52 .
(a) A light-rail commuter train accelerates at a rate of 1.35 m/s2. How long does it take to achieve its top speed of 80.0 km/h, starting from residual? (b) The same train ordinarily decelerates at a rate of i.65 g/s2. How long does it take to come to a stop from its superlative speed? (c) In emergencies, the train can decelerate more rapidly, coming to rest from 80.0 km/h in 8.thirty south. What is its emergency dispatch in meters per second squared?
53.
While inbound a freeway, a car accelerates from residue at a charge per unit of 2.04 m/stwo for 12.0 s. (a) Draw a sketch of the situation. (b) List the knowns in this problem. (c) How far does the car travel in those 12.0 s? To solve this function, start identify the unknown, then bespeak how you chose the appropriate equation to solve for information technology. After choosing the equation, evidence your steps in solving for the unknown, check your units, and discuss whether the respond is reasonable. (d) What is the car's final velocity? Solve for this unknown in the aforementioned manner as in (c), showing all steps explicitly.
54 .
Unreasonable results At the terminate of a race, a runner decelerates from a velocity of ix.00 yard/s at a charge per unit of 2.00 grand/due southtwo. (a) How far does she travel in the next 5.00 s? (b) What is her final velocity? (c) Evaluate the consequence. Does it brand sense?
55.
Blood is accelerated from rest to 30.0 cm/s in a altitude of one.eighty cm by the left ventricle of the eye. (a) Make a sketch of the situation. (b) List the knowns in this problem. (c) How long does the dispatch take? To solve this part, first identify the unknown, then discuss how you lot chose the appropriate equation to solve for it. After choosing the equation, show your steps in solving for the unknown, checking your units. (d) Is the respond reasonable when compared with the time for a heartbeat?
56 .
During a slap shot, a hockey player accelerates the puck from a velocity of 8.00 k/due south to forty.0 grand/s in the same direction. If this shot takes 3.33 × 10 − two s 3.33×10−2s , what is the distance over which the puck accelerates?
57.
A powerful motorbike can advance from rest to 26.eight m/s (100 km/h) in only iii.xc s. (a) What is its average acceleration? (b) How far does it travel in that time?
58 .
Freight trains can produce only relatively small accelerations. (a) What is the final velocity of a freight train that accelerates at a rate of 0.0500 m/s 2 0.0500m/s2 for eight.00 min, starting with an initial velocity of 4.00 chiliad/s? (b) If the train tin slow downwards at a rate of 0.550 m/south 2 0.550m/s2 , how long volition it take to come up to a stop from this velocity? (c) How far volition it travel in each instance?
59.
A fireworks crush is accelerated from rest to a velocity of 65.0 m/s over a distance of 0.250 m. (a) Calculate the dispatch. (b) How long did the acceleration last?
sixty .
A swan on a lake gets airborne by flapping its wings and running on summit of the water. (a) If the swan must reach a velocity of 6.00 m/s to take off and it accelerates from rest at an boilerplate rate of 0.35 m/southward two 0.35m/s2 , how far will it travel before condign airborne? (b) How long does this take?
61.
A woodpecker'due south encephalon is peculiarly protected from big accelerations past tendon-similar attachments inside the skull. While pecking on a tree, the woodpecker's caput comes to a stop from an initial velocity of 0.600 k/s in a distance of only ii.00 mm. (a) Find the acceleration in meters per second squared and in multiples ofm, whereg = 9.lxxx m/southwardii. (b) Summate the stopping time. (c) The tendons cradling the brain stretch, making its stopping distance 4.fifty mm (greater than the caput and, hence, less acceleration of the brain). What is the brain's dispatch, expressed in multiples ofg?
62 .
An unwary football histrion collides with a padded goalpost while running at a velocity of 7.l g/s and comes to a full stop later compressing the padding and his trunk 0.350 m. (a) What is his acceleration? (b) How long does the standoff last?
63.
A intendance package is dropped out of a cargo plane and lands in the forest. If we assume the care parcel speed on impact is 54 m/s (123 mph), so what is its dispatch? Presume the trees and snow stops it over a distance of three.0 m.
64 .
An express train passes through a station. It enters with an initial velocity of 22.0 m/s and decelerates at a charge per unit of 0.150 thousand/s 2 0.150m/s2 as it goes through. The station is 210.0 m long. (a) How fast is it going when the nose leaves the station? (b) How long is the olfactory organ of the railroad train in the station? (c) If the train is 130 m long, what is the velocity of the end of the railroad train as information technology leaves? (d) When does the end of the train go out the station?
65.
Unreasonable results Dragsters tin can actually reach a meridian speed of 145.0 m/s in only 4.45 s. (a) Calculate the average acceleration for such a dragster. (b) Find the last velocity of this dragster starting from rest and accelerating at the charge per unit found in (a) for 402.0 1000 (a quarter mile) without using any information on time. (c) Why is the last velocity greater than that used to notice the average acceleration? (Hint: Consider whether the assumption of constant acceleration is valid for a dragster. If not, discuss whether the dispatch would be greater at the beginning or end of the run and what effect that would accept on the last velocity.)
3.5 Gratuitous Fall
66 .
Calculate the deportation and velocity at times of (a) 0.500 s, (b) 1.00 s, (c) 1.fifty s, and (d) 2.00 s for a ball thrown direct up with an initial velocity of 15.0 m/due south. Have the point of release to exist y 0 = 0 y0=0 .
67.
Calculate the displacement and velocity at times of (a) 0.500 due south, (b) 1.00 s, (c) i.50 s, (d) two.00 southward, and (east) 2.l s for a stone thrown straight down with an initial velocity of 14.0 m/s from the Verrazano Narrows Bridge in New York Urban center. The roadway of this span is 70.0 chiliad above the water.
68 .
A basketball referee tosses the ball direct up for the starting tip-off. At what velocity must a basketball game histrion exit the ground to rise 1.25 g above the floor in an attempt to get the brawl?
69.
A rescue helicopter is hovering over a person whose boat has sunk. Ane of the rescuers throws a life preserver straight down to the victim with an initial velocity of one.40 m/s and observes that information technology takes ane.viii southward to reach the water. (a) List the knowns in this problem. (b) How high to a higher place the water was the preserver released? Note that the downdraft of the helicopter reduces the effects of air resistance on the falling life preserver, and so that an dispatch equal to that of gravity is reasonable.
70 .
Unreasonable results A dolphin in an aquatic show jumps straight up out of the water at a velocity of 15.0 thou/s. (a) Listing the knowns in this problem. (b) How high does his body rise higher up the h2o? To solve this role, first note that the final velocity is at present a known, and place its value. And so, place the unknown and discuss how yous chose the advisable equation to solve for information technology. After choosing the equation, bear witness your steps in solving for the unknown, checking units, and talk over whether the answer is reasonable. (c) How long a fourth dimension is the dolphin in the air? Neglect any effects resulting from his size or orientation.
71.
A diver bounces directly upwardly from a diving board, fugitive the diving lath on the way down, and falls anxiety starting time into a pool. She starts with a velocity of 4.00 m/due south and her takeoff point is 1.lxxx m above the puddle. (a) What is her highest point to a higher place the board? (b) How long a fourth dimension are her feet in the air? (c) What is her velocity when her feet hit the h2o?
72 .
(a) Calculate the height of a cliff if information technology takes 2.35 s for a stone to hit the ground when it is thrown straight upwardly from the cliff with an initial velocity of 8.00 thousand/s. (b) How long a time would it have to reach the footing if it is thrown straight downwardly with the same speed?
73.
A very strong, but inept, shot doodle puts the shot direct up vertically with an initial velocity of 11.0 m/s. How long a time does he accept to get out of the way if the shot was released at a elevation of two.xx yard and he is 1.eighty chiliad tall?
74 .
You throw a ball straight upward with an initial velocity of 15.0 m/due south. It passes a tree co-operative on the way up at a meridian of 7.0 m. How much additional time elapses before the ball passes the tree branch on the style dorsum down?
75.
A kangaroo tin jump over an object two.50 m high. (a) Considering merely its vertical motility, summate its vertical speed when it leaves the footing. (b) How long a time is it in the air?
76 .
Standing at the base of one of the cliffs of Mt. Arapiles in Victoria, Australia, a hiker hears a stone suspension loose from a height of 105.0 m. He can't see the rock right away, only then does, 1.50 south later. (a) How far in a higher place the hiker is the stone when he tin can see it? (b) How much time does he have to motion before the stone hits his caput?
77.
There is a 250-thou-high cliff at Half Dome in Yosemite National Park in California. Suppose a boulder breaks loose from the acme of this cliff. (a) How fast will it be going when it strikes the ground? (b) Bold a reaction time of 0.300 s, how long a time will a tourist at the bottom have to go out of the fashion later hearing the sound of the rock breaking loose (neglecting the tiptop of the tourist, which would become negligible anyway if hit)? The speed of sound is 335.0 thousand/due south on this day.
3.6 Finding Velocity and Displacement from Dispatch
78 .
The acceleration of a particle varies with time according to the equation a ( t ) = p t ii − q t 3 a(t)=pt2−qt3 . Initially, the velocity and position are nix. (a) What is the velocity equally a part of time? (b) What is the position every bit a function of time?
79.
Betwixtt = 0 andt =t 0, a rocket moves straight upward with an acceleration given by a ( t ) = A − B t 1 / two a(t)=A−Bt1/ii , whereA andBare constants. (a) If10 is in meters andt is in seconds, what are the units ofA andB? (b) If the rocket starts from residue, how does the velocity vary betweent = 0 andt =t 0? (c) If its initial position is zero, what is the rocket's position as a function of fourth dimension during this same time interval?
80 .
The velocity of a particle moving forth the10-axis varies with time according to v ( t ) = A + B t −ane v(t)=A+Bt−1 , whereA = 2 m/s,B = 0.25 m, and ane.0 s ≤ t ≤ 8.0 s i.0s≤t≤8.0s . Determine the dispatch and position of the particle att = 2.0 s andt = 5.0 due south. Presume that ten ( t = 1 s ) = 0 x(t=1s)=0 .
81.
A particle at rest leaves the origin with its velocity increasing with fourth dimension according to5(t) = iii.2t m/south. At 5.0 s, the particle's velocity starts decreasing according to [16.0 – 1.five(t – v.0)] m/south. This subtract continues untilt = 11.0 s, after which the particle's velocity remains constant at 7.0 yard/south. (a) What is the acceleration of the particle as a function of time? (b) What is the position of the particle att = two.0 s,t = 7.0 due south, andt = 12.0 due south?
Additional Bug
82 .
Professional baseball histrion Nolan Ryan could pitch a baseball at approximately 160.0 km/h. At that average velocity, how long did it take a ball thrown by Ryan to accomplish home plate, which is eighteen.four one thousand from the pitcher'south mound? Compare this with the average reaction time of a human to a visual stimulus, which is 0.25 south.
83.
An airplane leaves Chicago and makes the 3000-km trip to Los Angeles in 5.0 h. A second plane leaves Chicago half hour later on and arrives in Los Angeles at the same time. Compare the boilerplate velocities of the two planes. Ignore the curvature of Earth and the difference in altitude between the 2 cities.
84 .
Unreasonable Results A cyclist rides sixteen.0 km due east, then 8.0 km west, and so viii.0 km east, then 32.0 km west, and finally 11.two km east. If his average velocity is 24 km/h, how long did it have him to complete the trip? Is this a reasonable time?
85.
An object has an acceleration of + one.2 cm/s 2 +one.2cm/s2 . At t = iv.0 s t=four.0s , its velocity is − three.4 cm/s −3.4cm/due south . Decide the object's velocities at t = ane.0 s t=1.0s and t = half-dozen.0 s t=6.0s .
86 .
A particle moves along thex-axis according to the equation x ( t ) = ii.0 − 4.0 t ii 10(t)=2.0−four.0t2 yard. What are the velocity and acceleration at t = 2.0 t=2.0 s and t = 5.0 t=v.0 s?
87.
A particle moving at constant acceleration has velocities of ii.0 m/s ii.0m/s at t = 2.0 t=ii.0 s and − vii.six thou/due south −7.6m/s at t = 5.2 t=5.2 s. What is the dispatch of the particle?
88 .
A railroad train is moving up a steep grade at constant velocity (see following figure) when its caboose breaks loose and starts rolling freely along the track. Afterwards 5.0 due south, the caboose is thirty m behind the railroad train. What is the acceleration of the caboose?
89.
An electron is moving in a straight line with a velocity of 4.0 × 10 five 4.0×105 m/s. It enters a region five.0 cm long where information technology undergoes an acceleration of 6.0 × 10 12 thou/s ii half-dozen.0×1012m/s2 forth the same straight line. (a) What is the electron's velocity when it emerges from this region? b) How long does the electron accept to cantankerous the region?
90 .
An ambulance driver is rushing a patient to the infirmary. While traveling at 72 km/h, she notices the traffic light at the upcoming intersections has turned bister. To reach the intersection before the lite turns cerise, she must travel 50 m in 2.0 due south. (a) What minimum dispatch must the ambulance accept to reach the intersection before the light turns red? (b) What is the speed of the ambulance when it reaches the intersection?
91.
A motorcycle that is slowing down uniformly covers 2.0 successive km in eighty s and 120 due south, respectively. Summate (a) the acceleration of the motorbike and (b) its velocity at the get-go and end of the ii-km trip.
92 .
A cyclist travels from point A to point B in 10 min. During the first 2.0 min of her trip, she maintains a uniform acceleration of 0.090 m/south 2 0.090m/s2 . She then travels at constant velocity for the side by side 5.0 min. Next, she decelerates at a constant rate so that she comes to a balance at point B 3.0 min later. (a) Sketch the velocity-versus-time graph for the trip. (b) What is the acceleration during the last three min? (c) How far does the cyclist travel?
93.
2 trains are moving at 30 m/s in reverse directions on the same track. The engineers see simultaneously that they are on a collision course and apply the brakes when they are k m autonomously. Assuming both trains accept the same acceleration, what must this acceleration exist if the trains are to finish just short of colliding?
94 .
A x.0-thousand-long truck moving with a constant velocity of 97.0 km/h passes a 3.0-m-long car moving with a constant velocity of 80.0 km/h. How much time elapses between the moment the front of the truck is even with the back of the car and the moment the dorsum of the truck is fifty-fifty with the front of the car?
95.
A police car waits in hiding slightly off the highway. A speeding auto is spotted past the law car doing xl m/southward. At the instant the speeding car passes the law car, the police motorcar accelerates from rest at iv m/sii to grab the speeding car. How long does it have the law motorcar to catch the speeding car?
96 .
Pablo is running in a one-half marathon at a velocity of three yard/southward. Another runner, Jacob, is 50 meters behind Pablo with the same velocity. Jacob begins to accelerate at 0.05 thousand/s2. (a) How long does information technology take Jacob to take hold of Pablo? (b) What is the distance covered by Jacob? (c) What is the final velocity of Jacob?
97.
Unreasonable results A runner approaches the finish line and is 75 m abroad; her average speed at this position is eight m/southward. She decelerates at this point at 0.5 m/s2. How long does information technology accept her to cross the finish line from 75 m away? Is this reasonable?
98 .
An aeroplane accelerates at 5.0 m/due south2 for 30.0 s. During this fourth dimension, it covers a altitude of ten.0 km. What are the initial and terminal velocities of the airplane?
99.
Compare the distance traveled of an object that undergoes a alter in velocity that is twice its initial velocity with an object that changes its velocity by four times its initial velocity over the same time menstruation. The accelerations of both objects are constant.
100 .
An object is moving east with a constant velocity and is at position x 0 at time t 0 = 0 x0attimet0=0 . (a) With what dispatch must the object have for its full deportation to be aught at a later timet ? (b) What is the concrete interpretation of the solution in the case for t → ∞ t→∞ ?
101.
A ball is thrown straight upwardly. It passes a 2.00-yard-high window vii.50 grand off the ground on its path up and takes ane.30 s to become by the window. What was the ball's initial velocity?
102 .
A coin is dropped from a hot-air airship that is 300 m above the ground and rising at 10.0 m/due south upward. For the coin, find (a) the maximum peak reached, (b) its position and velocity iv.00 s after being released, and (c) the fourth dimension earlier it hits the ground.
103.
A soft tennis ball is dropped onto a hard floor from a superlative of 1.50 m and rebounds to a height of 1.ten m. (a) Summate its velocity just earlier it strikes the floor. (b) Calculate its velocity just after information technology leaves the floor on its fashion back upward. (c) Calculate its dispatch during contact with the floor if that contact lasts 3.l ms ( 3.50 × 10 − iii due south ) (three.50×ten−3s) (d) How much did the brawl compress during its collision with the flooring, assuming the floor is absolutely rigid?
104 .
Unreasonable results. A raindrop falls from a cloud 100 thousand above the ground. Neglect air resistance. What is the speed of the raindrop when it hits the ground? Is this a reasonable number?
105.
Compare the time in the air of a basketball game actor who jumps one.0 m vertically off the floor with that of a role player who jumps 0.3 m vertically.
106 .
Suppose that a person takes 0.v due south to react and move his manus to catch an object he has dropped. (a) How far does the object fall on Globe, where g = 9.eight m/southward 2 ? g=ix.8m/s2? (b) How far does the object autumn on the Moon, where the acceleration due to gravity is 1/6 of that on World?
107.
A gasbag airship rises from ground level at a abiding velocity of 3.0 one thousand/s. Ane infinitesimal afterward liftoff, a sandbag is dropped accidentally from the balloon. Calculate (a) the fourth dimension it takes for the sandbag to achieve the basis and (b) the velocity of the sandbag when it hits the ground.
108 .
(a) A earth tape was ready for the men'due south 100-thousand dash in the 2008 Olympic Games in Beijing by Usain Bolt of Jamaica. Bolt "coasted" across the terminate line with a time of nine.69 south. If nosotros presume that Bolt accelerated for three.00 s to reach his maximum speed, and maintained that speed for the balance of the race, summate his maximum speed and his dispatch. (b) During the same Olympics, Bolt also set the world tape in the 200-chiliad dash with a time of 19.thirty s. Using the same assumptions as for the 100-m nuance, what was his maximum speed for this race?
109.
An object is dropped from a top of 75.0 m higher up ground level. (a) Make up one's mind the altitude traveled during the first second. (b) Determine the final velocity at which the object hits the ground. (c) Determine the distance traveled during the last second of motion earlier hit the ground.
110 .
A steel brawl is dropped onto a difficult flooring from a height of 1.50 m and rebounds to a superlative of ane.45 1000. (a) Calculate its velocity but earlier it strikes the floor. (b) Calculate its velocity simply after it leaves the floor on its mode back up. (c) Calculate its acceleration during contact with the floor if that contact lasts 0.0800 ms ( 8.00 × 10 − five s ) (8.00×10−5s) (d) How much did the ball compress during its collision with the floor, assuming the flooring is absolutely rigid?
111.
An object is dropped from a roof of a building of heighth. During the concluding 2d of its descent, it drops a distanceh/3. Calculate the acme of the building.
Challenge Problems
112 .
In a 100-m race, the winner is timed at xi.2 s. The second-identify finisher'southward fourth dimension is xi.half-dozen s. How far is the second-place finisher behind the winner when she crosses the finish line? Presume the velocity of each runner is constant throughout the race.
113.
The position of a particle moving along thex-axis varies with time according to ten ( t ) = 5.0 t 2 − 4.0 t 3 x(t)=v.0t2−4.0t3 m. Observe (a) the velocity and dispatch of the particle as functions of time, (b) the velocity and acceleration att = ii.0 s, (c) the time at which the position is a maximum, (d) the fourth dimension at which the velocity is zero, and (e) the maximum position.
114 .
A cyclist sprints at the end of a race to clinch a victory. She has an initial velocity of xi.5 m/due south and accelerates at a rate of 0.500 m/s2 for seven.00 s. (a) What is her final velocity? (b) The cyclist continues at this velocity to the terminate line. If she is 300 g from the finish line when she starts to advance, how much fourth dimension did she save? (c) The second-identify winner was 5.00 1000 ahead when the winner started to accelerate, but he was unable to advance, and traveled at eleven.8 m/s until the finish line. What was the deviation in finish time in seconds between the winner and runner-upward? How far back was the runner-up when the winner crossed the finish line?
115.
In 1967, New Zealander Burt Munro fix the earth tape for an Indian motorcycle, on the Bonneville Table salt Flats in Utah, of 295.38 km/h. The one-way class was 8.00 km long. Acceleration rates are ofttimes described past the time it takes to achieve 96.0 km/h from rest. If this time was 4.00 s and Burt accelerated at this rate until he reached his maximum speed, how long did it take Burt to complete the class?
Source: https://opentextbc.ca/universityphysicsv1openstax/chapter/3-chapter-review/
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