Help on basic physics questions? (kinematics)?

Question

1). At a given instant of time, a car and a truck are traveling side by side in adjacent lanes of a highway. The car has a greater velocity than the truck. Does the car necessarily have a greater acceleration? Explain.

2). 2 objects are thrown vertically upward, first one, and then, later, the other. Is it possible that both reach the same maximum height at the same instant? Explain.

3). A runner runs half the remaining distance to the finish line every ten seconds. She runs in a straight line and does not reverse her direction. Does her acceleration have a constant magnitude? Explain.

Thank you for your help! Also, by looking at my questions, there are evidently some holes in my conceptual understanding, so any pointers about the key concepts that I should make sure that I know would be helpful too. Thanks again!

Answer 1

no, all you know is that the car has a greater velocity, which tells you nothing about the acceleration.

yes, if you toss the first one higher than the second.

no, her acceleration is changing. The distance changes every 10 seconds, the time does not. Example, mid point is 128 ft from end.

first 10 seconds, 64' in 10 sec -- V = 6.4 ft/s

sec 10 seconds, 32' in 10 sec -- V = 3.2 ft/s

thrd 10 seconds, 16' in 10 sec -- V = 1.6 ft/s

frth 10 seconds, 8' in 10 sec -- V = 0.8 ft/s

fifth 10 seconds, 4' in 10 sec -- V = 0.4 ft/s

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.

Assuming velocity changes smoothly in that interval, than accelerations are

1-2 period, A = (6.4-3.2)/10 ft/s² = 0.32 ft/s²

2-3 period, A = (3.2-1.6)/10 ft/s² = 0.16 ft/s²

3-4 period, A = (1.6-0.8)/10 ft/s² = 0.08 ft/s²

4-5 period, A = (0.8-0.4)/10 ft/s² = 0.04 ft/s²

so from the example, acceleration is changing.