Q: A car moves from $$x_1 = -3.0$$\ \mathrm{m}$$ to x_2$ = 5.0\ \mathrm{m}$$ along a straight road. What is the displacement and the distance traveled by the car?

$$\text{Displacement} = 8.0\ \mathrm{m},\ \text{Distance} = 8.0\ \mathrm{m}$$

Q: A runner completes one lap around a 400 m track, starting and ending at the same point. What are the runner’s displacement and distance?

$$\text{Displacement} = 0\ \mathrm{m},\ \text{Distance} = 400\ \mathrm{m}$$

Q: A car starts at $$x_0 = 0$ with v_0$ = 10\ \mathrm{m/s}$$ and accelerates at $$a = 2\ \mathrm{m/s^2$}$$ for $$t = 5\ \mathrm{s}. $$What is its final position?

$$x = 10\ \mathrm{m/s} \times 5\ \mathrm{s} + \frac{1}{2} \times 2\ \mathrm{m/s^2$} \times (5\ \mathrm{s})^2$ = 10 \times 5 + 0.5 \times 2 \times 25 = 50 + 25 = 75\ \mathrm{m}$$

Question 1

A car moves from $$x_1 = -3.0$$\ \mathrm{m}$$ to x_2$ = 5.0\ \mathrm{m}$$ along a straight road. What is the displacement and the distance traveled by the car?

Accepted Answer

$$	ext{Displacement} = 8.0\ \mathrm{m},\ 	ext{Distance} = 8.0\ \mathrm{m}$$

Question 2

Which of the following best describes the difference between distance and displacement?

Accepted Answer

Distance is a scalar and displacement is a vector.

Question 3

A runner completes one lap around a 400 m track, starting and ending at the same point. What are the runner’s displacement and distance?

Accepted Answer

$$	ext{Displacement} = 0\ \mathrm{m},\ 	ext{Distance} = 400\ \mathrm{m}$$

Question 4

A car moves with a constant velocity of $$15\ \mathrm{m/s}$$ for $$10\ \mathrm{s}. $$What is its displacement?

Accepted Answer

$$150\ \mathrm{m}$$

Question 5

Which of the following statements about reference frames is correct?

Accepted Answer

The description of motion depends on the observer’s reference frame.

Question 6

A velocity-versus-time graph for an object moving at constant velocity is:

Accepted Answer

A horizontal straight line.

Question 7

A ball is dropped from rest and falls freely under gravity. What is the acceleration of the ball (neglecting air resistance)?

Accepted Answer

$$9.8\ \mathrm{m/s^2$}$$\ downward

Question 8

Which equation gives the position $$x of an $$object moving with constant acceleration $$a$$ and initial velocity $$v_0$$ after time $$t$$?

Accepted Answer

$$x = x_0$ + v_0$ t + \frac{1}{2} a t^2$

Question 9

A car starts from rest and accelerates uniformly at $$2.0\ \mathrm{m/s^2$}$$ for $$5.0\ \mathrm{s}. $$What is its final velocity?

Accepted Answer

$$v = 10\ \mathrm{m/s}$$

Question 10

A cyclist rides east at $$8\ \mathrm{m/s}$$ for $$10\ \mathrm{s}$$, then west at $$4\ \mathrm{m/s}$$ for $$5\ \mathrm{s}. $$What is the total displacement?

Accepted Answer

$$60\ \mathrm{m}$$\ east

Question 11

Which of the following is true about the area under a velocity-versus-time graph?

Accepted Answer

It represents the displacement of the object.

Question 12

A car moves with a velocity given by $$v_x = 5.0\ \mathrm{m/s}$$ for $$t = 0 to$$ $$t = 4.0\ \mathrm{s}. $$What is the area under the velocity-time graph during this interval?

Accepted Answer

$$20\ \mathrm{m}$$

Question 13

Which of the following best describes the meaning of 'motion is relative'?

Accepted Answer

The motion of an object depends on the observer’s reference frame.

Question 14

A car travels at $$20\ \mathrm{m/s}$$ for $$3.0\ \mathrm{s}$$, then at $$10\ \mathrm{m/s}$$ for $$2.0\ \mathrm{s}. $$What is the average velocity for the entire trip?

Accepted Answer

$$16\ \mathrm{m/s}$$

Question 15

Which of the following is the correct equation for average acceleration $$a$$?

Accepted Answer

$$a = \frac{v_f - v_i}{t_f - t_i}$$

Question 16

A ball is thrown straight up with an initial velocity of $$12\ \mathrm{m/s}. $$How long does it take to reach its highest point? (Assume $$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

$$1.22\ \mathrm{s}$$

Question 17

Which of the following is NOT a valid way to represent motion?

Accepted Answer

A chemical equation

Question 18

A car starts at $$x_0 = 0$ with v_0$ = 10\ \mathrm{m/s}$$ and accelerates at $$a = 2\ \mathrm{m/s^2$}$$ for $$t = 5\ \mathrm{s}. $$What is its final position?

Accepted Answer

$$x = 10\ \mathrm{m/s} 	imes 5\ \mathrm{s} + \frac{1}{2} 	imes 2\ \mathrm{m/s^2$} 	imes (5\ \mathrm{s})^2$ = 10 	imes 5 + 0.5 	imes 2 	imes 25 = 50 + 25 = 75\ \mathrm{m}$$

Kinematics: Motion in One Dimension – Study Notes

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