Q: A runner completes a lap around a 400-meter track, starting and ending at the same point. Which statement best describes the runner's displacement after one lap?

The displacement is $$0\ \text{meters}.$$

Q: A car travels 60 meters east, then 80 meters west, and finally 140 meters east. What is the total distance traveled and the displacement?

Total distance: $$280\ \text{meters}$$, Displacement: $$120\ \text{meters}$$ east

Q: If a cyclist moves from point A to point B, a distance of $$20\ \text{meters}$$ north, in $$3\ \text{seconds}$$, what is the average velocity?

$$\frac{20}{3}\ \text{m/s}$$ north

Q: After eating dinner at The Top, you walk a path of $$60\ \text{meters}$$, then $$80\ \text{meters}$$, and finally $$140\ \text{meters}$$, taking $$10\ \text{minutes} in $$total. What is your average speed?

$$\frac{60+80+140}{10\times 60}\ \text{m/s} = \frac{280}{600}\ \text{m/s} \approx 0.47\ \text{m/s}$$

Q: A student walks $$80\ \text{meters}$$ east in $$4\ \text{minutes}$$, then $$60\ \text{meters}$$ west in $$2\ \text{minutes}. $$What is the average velocity for the entire trip?

$$\frac{80-60}{4+2}\ \text{m/min} = \frac{20}{6}\ \text{m/min} \approx 3.33\ \text{m/min}$$ east

Q: A car starts from rest and accelerates at $$3\ \text{m/s}^2$$ for $$5\ \text{seconds}. $$What is its final velocity?

$$v = a t = 3 \times 5 = 15\ \text{m/s}$$

Q: A Boeing 747 accelerates at $$2.6\ \text{m/s}^2$$ from rest to a takeoff speed of $$70\ \text{m/s}. $$How much time does it take to reach takeoff speed?

$$t = \frac{v}{a} = \frac{70}{2.6} \approx 26.92\ \text{seconds}$$

Q: For the Boeing 747 in the previous question, what is the minimum length of runway required for takeoff?

$$d = \frac{1}{2} a t^2$ = \frac{1}{2} \times 2.6 \times (26.92)^2$ \approx 942\ \text{meters}$$

Question 1

A runner completes a lap around a 400-meter track, starting and ending at the same point. Which statement best describes the runner's displacement after one lap?

Accepted Answer

The displacement is $$0\ 	ext{meters}.$$

Question 2

A car travels 60 meters east, then 80 meters west, and finally 140 meters east. What is the total distance traveled and the displacement?

Accepted Answer

Total distance: $$280\ 	ext{meters}$$, Displacement: $$120\ 	ext{meters}$$ east

Question 3

If a cyclist moves from point A to point B, a distance of $$20\ 	ext{meters}$$ north, in $$3\ 	ext{seconds}$$, what is the average velocity?

Accepted Answer

$$\frac{20}{3}\ 	ext{m/s}$$ north

Question 4

After eating dinner at The Top, you walk a path of $$60\ 	ext{meters}$$, then $$80\ 	ext{meters}$$, and finally $$140\ 	ext{meters}$$, taking $$10\ 	ext{minutes} in $$total. What is your average speed?

Accepted Answer

$$\frac{60+80+140}{10	imes 60}\ 	ext{m/s} = \frac{280}{600}\ 	ext{m/s} \approx 0.47\ 	ext{m/s}$$

Question 5

On a position vs. time graph, the slope of the line represents:

Accepted Answer

The object's velocity

Question 6

A student walks $$80\ 	ext{meters}$$ east in $$4\ 	ext{minutes}$$, then $$60\ 	ext{meters}$$ west in $$2\ 	ext{minutes}. $$What is the average velocity for the entire trip?

Accepted Answer

$$\frac{80-60}{4+2}\ 	ext{m/min} = \frac{20}{6}\ 	ext{m/min} \approx 3.33\ 	ext{m/min}$$ east

Question 7

Which of the following best describes instantaneous velocity?

Accepted Answer

The velocity at a specific moment in time

Question 8

On a velocity vs. time graph, what does the area under the curve represent?

Accepted Answer

The object's displacement

Question 9

A car starts from rest and accelerates at $$3\ 	ext{m/s}^2$$ for $$5\ 	ext{seconds}. $$What is its final velocity?

Accepted Answer

$$v = a t = 3 	imes 5 = 15\ 	ext{m/s}$$

Question 10

A Boeing 747 accelerates at $$2.6\ 	ext{m/s}^2$$ from rest to a takeoff speed of $$70\ 	ext{m/s}. $$How much time does it take to reach takeoff speed?

Accepted Answer

$$t = \frac{v}{a} = \frac{70}{2.6} \approx 26.92\ 	ext{seconds}$$

Question 11

For the Boeing 747 in the previous question, what is the minimum length of runway required for takeoff?

Accepted Answer

$$d = \frac{1}{2} a t^2$ = \frac{1}{2} 	imes 2.6 	imes (26.92)^2$ \approx 942\ 	ext{meters}$$

Question 12

A position vs. time graph shows a straight line with a positive slope. What does this indicate about the object's motion?

Accepted Answer

The object is moving at constant velocity in the positive direction.

Question 13

If the velocity vs. time graph is a horizontal line above the time axis, what is the object's acceleration?

Accepted Answer

Zero acceleration

Question 14

A car moves with constant acceleration. Which equation correctly relates displacement $$d$$, initial velocity $$v_0$$, acceleration $$a$$, and time $$t$$?

Accepted Answer

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

Question 15

A student throws a ball straight up. At the highest point, what is the instantaneous velocity of the ball?

Accepted Answer

Zero

Question 16

Which of the following statements about average speed and average velocity is correct?

Accepted Answer

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

Question 17

A car travels $$100\ 	ext{meters}$$ north, then $$100\ 	ext{meters}$$ south, in $$50\ 	ext{seconds}. $$What is its average velocity?

Accepted Answer

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

Question 18

If an object’s velocity changes from $$10\ 	ext{m/s} to$$ $$30\ 	ext{m/s} in$$ $$5\ 	ext{seconds}$$, what is its acceleration?

Accepted Answer

$$a = \frac{\Delta v}{\Delta t} = \frac{30-10}{5} = 4\ 	ext{m/s}^2$$

Question 19

A train moves at $$20\ 	ext{m/s}$$ for $$10\ 	ext{seconds}$$, then stops instantly. What is the total displacement?

Accepted Answer

$$d = v t = 20 	imes 10 = 200\ 	ext{meters}$$

Describing Motion: Position, Velocity, and Acceleration (Ch 2.1–2.4)

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