1. Initially, a ball has a speed of 5.0 m/s as it rolls up an incline. Some time later, at a distance of 5.5 m up the incline, the ball has a speed of 1.5 m/s DOWN the incline. (a) What is the acceleration? What is the average velocity? How much time did this take? (b) At some point the velocity of the ball had to have been zero. Where and when did this occur?

1. Initially, a ball has a speed of 5.0 m/s as it rolls up an incline. Some time later, at a distance of 5.5 m up the incline, the ball has a speed of 1.5 m/s DOWN the incline. (a) What is the acceleration? What is the average velocity? How much time did this take? (b) At some point the velocity of the ball had to have been zero. Where and when did this occur?

An Introduction to Physical Science

14th Edition

ISBN:9781305079137

Author:James Shipman, Jerry D. Wilson, Charles A. Higgins, Omar Torres

Publisher:James Shipman, Jerry D. Wilson, Charles A. Higgins, Omar Torres

Chapter2: Motion

Section: Chapter Questions

Problem 14E: A car travels on a straight, level road. (a) Starting from rest, the car is going 44 ft/s (30 mi/h)...

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A car travels on a straight, level road. (a) Starting from rest, the car is going 44 ft/s (30 mi/h) at the end of 5.0 s. What is the cars average acceleration in ft/s2? (b) In 4.0 more seconds, the car is going 88 ft/s (60 mi/h). What is the cars average acceleration for this time period? (c) The car then slows to 66 ft/s (45 mi/h) in 3.0 s. What is the average acceleration for this time period? (d) What is the overall average acceleration for the total time? (Note these convenient British unit conversions: 60 mi/h = 88 ft/s, 45 mi/h = 66 ft/s, and 30 mi/h = 44 ft/s.)
3. A car travels along a straight line at a constant speed of 72.0 km/h for a distance x and then another distance 2x in the same direction at another constant speed of 36.0 km/h. (a) What is the average speed and average velocity for this trip? 4. At t = 0, one car is rolling on a straight-line initial position 10.0 m, initial velocity 5 m/s, and constant acceleration 3.0 m/s². At the same moment, another car is set rolling on an adjacent track with initial position 50 m, initial velocity 72 km/hour, and zero acceleration. (a) At what time, if any, do the two cars have equal speeds? (d) What are their locations at that time?
6. A nut comes loose from a bolt on the bottom of an elevator, as the elevator is moving up the shaft at 3.00 m/s. The nut strikes the bottom of the shaft in 2.00 s. (a) How far from the bottom of the shaft was the elevator when the nut fell off? (b) How far above the bottom was the nut 0.25 s after it fell off? Answer: 13.6m, 14 m
2. A particle moves along the x-axis according to the equation X = 5.00 + 7.00t – 2.00t2, where x is in meters and t is in seconds. (a) What is the particle's position along the x-axis at t= 3.00-s? (b) What is the particle's average velocity between t = 0 and t= 3.00-s? (c) At what time is the particle's average velocity zero (other than at t-0)? (d) What is the particle's average acceleration between t = 0 and t = 3.00-s? (e) What is the particle's instantaneous velocity at t = 3.00-s? Answers: (a) 8.00 m (b) 1.00 m/s (c) 3.50 s (d) -4.00 m/s² (e) -5.00 m/s
3. A car's velocity as a function of time is given by vy= 2 = a+ br?, where a = 3.00 m/s and b= 0.100 m/s. (a) Calculate the average acceleration for the time interval 1= 0 to 1 = 5.00 s. (b) Calculate the instantaneous acceleration for t= 0 and t= 5.00 s.
2. A ball is thrown upwards from height ho with velocity v0. Ignoring air resistance, the acceleration is given by a(t) = -32. Recall that h'(t) = v(t) and v'(t) = a(t). (a) Find the height h(t) of the ball at time t. (b) Find the time at which the ball reaches its maximum height. (c) Find the maximum height.
1. Starting from a pillar, you run 200 m east (the +x-direction) at an average speed of 5.0 m/s, and then run 280 m west at an average speed of 4.0 m/s to a post. Calculate (a) your average speed from pillar to post and (b) your average velocity from pillar to post.
8. At time t=0, a ball is thrown vertically upward from the ground level, reaching its maximum height and returning back to the ground level. Which velocity versus time graph describes its motion? Take the upward direction as the positive direction. (a) WITH (b) (b) 220 9. An airplane flying horizontally at a height h=80 m above the ground with a speed of v-70 m/s drops a package to hit a mark on the ground. At what distance a in m ahead of the mark should the pilot release the package? (a) 200 (c) 240 (d) (d) 260 (e) 280 ..... h
Does acceleration depend on the speed of an object? Why or why not? Give an example of a slow object having a larger acceleration than a fast object. Can anyone think of an example of an object moving in such a way so that it is accelerating while having zero velocity?
A bird is flying due east. Its distance from a tall building is given by x(t) = 28 m+ (12.4) t-(0.045) ³ t3 a. What is the velocity of the bird when t = 8 seconds? b. What is the acceleration of the bird when t = 8 seconds?
9. The acceleration of a particle as it moves along a straight line is given by a = (2t - 1) m/s, where t is in seconds. If s =1 m and v = 2 m/s when t 0, determine the particle's velocity and position when t= 6 s. Also, determine the total distance the particle travels during this time period. Ans: v = 32 m/s; s = 67 m; d = 66 m 10 A narticle moves along a straight line uvith an acceleration of a = 5/(3s!/3 + 5/2) m/s2 where s is in
3. a) A boy throws a stone straight upward with an initial speed of 15 m/s. What maximum height will the stone reach before falling back down? b) What would be the maximum height of the stone if the boy and the stone were on the surface of the Moon, where the acceleration due to gravity is only ⅙ that of the Earth’s?