Q: A police car starts from rest and accelerates at $$7.41\ \mathrm{m/s^2$}$$ for $$t$$ seconds. What is the distance covered in $$t$$ seconds?

$$x = \frac{1}{2} \times 7.41 \times t^2$

Question 1

Given the velocity-time graph of a basketball player moving in a straight line, what is the net displacement of the player over the 10 seconds shown?

Accepted Answer

$$18\ \mathrm{m}$$

Question 2

Based on the same velocity-time graph, what is the total distance run by the player during the 10 seconds?

Accepted Answer

$$20\ \mathrm{m}$$

Question 3

If the position of an object is given by $$x = 2t^2$ - ct$$, where $$c is a $$constant, what is the instantaneous velocity at $$t = 1\ \mathrm{s} if$$ $$c = 1.9$$?

Accepted Answer

$$2.1\ \mathrm{m/s}$$

Question 4

Given $$x = 3t^2$ + 7t + 2$$, what is the instantaneous acceleration at $$t = 1\ \mathrm{s}$$?

Accepted Answer

$$13\ \mathrm{m/s^2$}$$

Question 5

A car travels at a constant $$30.0\ \mathrm{m/s}$$ and passes a stationary police car. If the police car waits $$1.00\ \mathrm{s}$$ before starting, what constant acceleration must the police car have to catch up after traveling $$300\ \mathrm{m}$$?

Accepted Answer

$$7.41\ \mathrm{m/s^2$}$$

Question 6

A runner starts from rest and accelerates uniformly to a speed of $$9.00\ \mathrm{m/s}$$ over a distance of $$60.0\ \mathrm{m}. $$How much time does it take to cover this distance?

Accepted Answer

$$6.67\ \mathrm{s}$$

Question 7

Which area under the velocity-time graph corresponds to the displacement between $$t=0$$ and $$t=4\ \mathrm{s}$$?

Accepted Answer

The sum of the areas under segments A and B

Question 8

If the velocity-time graph dips below the time axis, what does the area under that section represent?

Accepted Answer

Negative displacement

Question 9

A car accelerates from rest at a constant rate. Which equation correctly relates the distance $$x$$, acceleration $$a$$, and time $$t$$?

Accepted Answer

$$x = \frac{1}{2} a t^2$

Question 10

If a runner's velocity changes from $$0 to$$ $$9.00\ \mathrm{m/s} in$$ $$6.67\ \mathrm{s}$$, what is her average acceleration?

Accepted Answer

$$1.35\ \mathrm{m/s^2$}$$

Question 11

A police car starts from rest and accelerates at $$7.41\ \mathrm{m/s^2$}$$ for $$t$$ seconds. What is the distance covered in $$t$$ seconds?

Accepted Answer

$$x = \frac{1}{2} 	imes 7.41 	imes t^2$

Question 12

If the area under the velocity-time graph from $$t=0 to$$ $$t=10\ \mathrm{s} is$$ $$18\ \mathrm{m}$$, what does this value represent?

Accepted Answer

Net displacement

Question 13

If the total distance run by the player is $$20\ \mathrm{m}$$ but the net displacement is $$18\ \mathrm{m}$$, what does this indicate about the player's motion?

Accepted Answer

The player changed direction during the motion

Question 14

Which kinematic equation would you use to find the time taken to travel a distance $$d$$ with initial velocity $$u=0$$ and final velocity $$v$$?

Accepted Answer

$$d = \frac{1}{2} (u + v) t$$

Analyzing Displacement and Distance from a Velocity-Time Graph

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