Question 1

Tim and Rick both can run at speed $$v_r$$ and walk at speed $$v_w$$, with $$v_r \u003e v_w. $$They set off together on a journey of distance $$D. $$Rick walks half of the distance and runs the other half. What is the total time $$t_{Rick} it $$takes Rick to cover the distance $$D$$?

Accepted Answer

$$t_{Rick} = \frac{D}{2v_w} + \frac{D}{2v_r}$$

Question 2

Given Rick's journey in the previous question, what is his average speed $$v_{avg}$$ for covering the distance $$D$$?

Accepted Answer

$$v_{avg} = \frac{2v_r v_w}{v_r + v_w}$$

Question 3

Tim walks at speed $$v_w$$ for half the time and runs at speed $$v_r$$ for the other half. What is the total time $$t_{Tim} it $$takes Tim to cover the distance $$D$$?

Accepted Answer

$$t_{Tim} = \frac{D}{\frac{v_r + v_w}{2}}$$

Question 4

A soccer player runs three sprints: 10 m out and back, 20 m out and back, and 30 m out and back. If the total time is 44.7 s, what is her average speed?

Accepted Answer

$$2.7\ \mathrm{m/s}$$

Question 5

For the same soccer player, what is her average velocity for the entire exercise?

Accepted Answer

$$0\ \mathrm{m/s}$$

Question 6

A car traveling due east at $$20\ \mathrm{m/s}$$ reverses its direction over a period of $$10\ \mathrm{s} so $$that it is now traveling due west at $$20\ \mathrm{m/s}. $$What is the direction of the car’s average acceleration over this period?

Accepted Answer

The car’s average acceleration points due west.

Question 7

A rock is thrown straight up with initial speed $$v_0$$ from the edge of a building of height $$h. $$What is the vertical component $$v_{avg,y} of $$its average velocity from the roof to the ground?

Accepted Answer

$$v_{avg,y} = -\frac{h}{t_{total}}$$

Question 8

Suppose you toss a rock upward so that it rises and then falls back to the earth. If the acceleration due to gravity is $$9.8\ \mathrm{m/s^2$}$$, what is the rock’s acceleration at the instant that it reaches the top of its trajectory?

Accepted Answer

The rock has a downward acceleration of $$9.8\ \mathrm{m/s^2$}.$$

Question 9

A man is running at speed $$v_m to $$catch a bus that starts accelerating from rest with acceleration $$a at a $$distance $$d$$ ahead. What is the minimum value of $$v_m$$ for which the man will catch the bus?

Accepted Answer

$$v_m = \sqrt{2ad}$$

Question 10

A skier slows down on dry snow with maximum (negative) acceleration $$a_{dry}$$, which is two-fifths that of wet snow $$a_{wet}. $$For a given initial velocity, how does the time $$t_{dry} to $$stop on dry snow compare to the time $$t_{wet} to $$stop on wet snow?

Accepted Answer

$$t_{dry} = \frac{5}{2} t_{wet}$$

Question 11

For the skier in the previous question, how does the stopping distance $$x_{dry} on $$dry snow compare to the stopping distance $$x_{wet} on $$wet snow?

Accepted Answer

$$x_{dry} = \frac{5}{2} x_{wet}$$

Question 12

Given the position vs. time graph for a physics professor walking to campus and returning home (see image), at which labeled point is her velocity zero?

Accepted Answer

IV

Question 13

Given the same graph, at which labeled point is her velocity constant and positive?

Accepted Answer

II

Question 14

Given the same graph, at which labeled point is her velocity constant and negative?

Accepted Answer

V

Question 15

Given the table of positions vs. time: $$x = 0, 1, 4, 9, 16, 24, 32, 40, 46, 48 at$$ $$t = 0 to$$ $$9 s$$, which position vs. time graph best represents the motion?

Accepted Answer

Graph 1 (smooth upward curve)

Question 16

For the same data, which velocity vs. time graph best represents the object's motion?

Accepted Answer

Graph 4 (increasing then decreasing)

Question 17

For the same data, which acceleration vs. time graph best represents the object's motion?

Accepted Answer

Graph 4 (triangle shape, positive then negative)

Study Guide: Motion Along a Straight Line – Graphs, Velocity, and Acceleration

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