Question 1

Which of the following statements best describes the difference between average speed and average velocity for an object moving along a straight path?

Accepted Answer

Average speed is the total distance traveled divided by time, while average velocity is the displacement divided by time.

Question 2

A sled moves from position $$\vec{r}_1 = (10\,\mathrm{m}, 30^\circ) at$$ $$t_1 = 3$$\,\mathrm{s}$$ to $$\vec{r}_2 = (21\,\mathrm{m}, 45^\circ)$$ at t_2$ = 4\,\mathrm{s}. $$What is the displacement vector $$\Delta \vec{r}$$?

Accepted Answer

$$\Delta \vec{r} = (11\,\mathrm{m}, 15^\circ)$$

Question 3

Which of the following is required for a quantity to be considered a vector?

Accepted Answer

It must have both magnitude and direction.

Question 4

Given two vectors $$\vec{P}$$ and $$\vec{Q}$$, which graphical method correctly represents $$\vec{P} + \vec{Q}$$?

Accepted Answer

Place the tail of $$\vec{Q} at $$the tip of $$\vec{P}$$ and draw an arrow from the tail of $$\vec{P} to $$the tip of $$\vec{Q}.$$

Question 5

A car travels 100 m east, then 50 m west in 30 seconds. What is its average velocity?

Accepted Answer

$$\frac{50\,\mathrm{m}}{30\,\mathrm{s}} = 1.67\,\mathrm{m/s}$$ east

Question 6

If an object’s velocity changes from $$v_i = 2\,\mathrm{m/s} to$$ $$v_f = 8\,\mathrm{m/s} in$$ $$3\,\mathrm{s}$$, what is its average acceleration?

Accepted Answer

$$a_{avg} = \frac{8 - 2}{3} = 2\,\mathrm{m/s^2$}$$

Question 7

A ball is tossed straight up in the air. At its very highest point, what is the direction of the acceleration vector?

Accepted Answer

It points down.

Question 8

Which of the following statements is true about the signs of position $$x$$ and velocity $$v$$ for a particle slowing down while moving in the positive direction?

Accepted Answer

Position is positive, and velocity is positive.

Question 9

A car moves to the left for 30 minutes, stops for 10 minutes, then moves to the right for 40 minutes. Which position-versus-time graph best represents this motion?

Accepted Answer

A graph with a negative slope, then a horizontal segment, then a positive slope.

Question 10

If an object is speeding up, what is the relationship between its velocity and acceleration vectors?

Accepted Answer

They point in the same direction.

Question 11

Which of the following is NOT a recommended step in solving physics problems?

Accepted Answer

Jumping directly to mathematical equations without modeling or visualizing.

Question 12

A particle moves with constant velocity. What can be said about its acceleration?

Accepted Answer

Its acceleration is zero.

Question 13

A stopwatch is used to measure a time interval $$\Delta t. If $$two observers use different clocks and coordinate systems, what will they find for $$\Delta t$$ and displacement $$\Delta \vec{r}$$?

Accepted Answer

They will find the same values for $$\Delta t$$ and $$\Delta \vec{r}.$$

Question 14

Which of the following best describes vector subtraction $$\vec{P} - \vec{Q}$$?

Accepted Answer

Add $$\vec{P} to $$the negative of $$\vec{Q}.$$

Question 15

A car moves along a straight line, stops, and then moves again. Which real-world scenario best matches this motion?

Accepted Answer

A car that drives and stops and drives and stops.

Question 16

A tortoise and a hare are racing. The motion diagram shows the tortoise moving at a constant speed and the hare accelerating. Which statement is true about their velocity vectors?

Accepted Answer

The tortoise’s velocity vectors are equal in length and direction; the hare’s velocity vectors increase in length.

Question 17

Which mathematical operation is used to find the average acceleration vector $$\vec{a}_{avg}$$?

Accepted Answer

$$\vec{a}_{avg} = \frac{\Delta \vec{v}}{\Delta t}$$

Question 18

A student walks to school at a constant speed. Which position-versus-time graph best represents her motion?

Accepted Answer

A straight line with a constant positive slope.

Kinematics and Vectors: Foundations of Motion in Physics

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