Q: A car travels 60 meters east, then 40 meters west. What is the car's total displacement?

$$\Delta x = 20\ \text{m}\ \text{east}$$

Q: A runner jogs 15 m forward in 2 s, then 9 m backward in another 2 s. What is the average velocity for the total trip?

$$v_{avg} = \frac{15\ \text{m} - 9\ \text{m}}{4\ \text{s}} = 1.5\ \text{m/s}$$

Q: A baseball pitcher throws a ball at 44 m/s toward home plate, which is 18.5 m away. How long does it take for the ball to reach home plate?

$$t = \frac{18.5\ \text{m}}{44\ \text{m/s}} = 0.42\ \text{s}$$

Q: A moving hockey puck encounters a patch of rough ice and slides 0.90 m before coming to a stop. If the deceleration is $$8.0\ \text{m/s}^2$$, what was the puck’s initial speed?

$$v_0$$ = \sqrt{2a\Delta x} = \sqrt{2 \times 8.0 \times 0.90} = 3.8\ \text{m/s}$$

Q: A rock is thrown upward with a speed of $$27.0\ \text{m/s}$$ from the roof of a $$31.0\ \text{m}$$ tall building. What is the speed of the rock just before it hits the street?

$$v = \sqrt{v_0$^2 + 2g\Delta y} = \sqrt{27.0^2$ + 2 \times 9.8 \times 31.0} = 36.6\ \text{m/s}$$

Q: A police car at rest is passed by a speeder traveling at a constant $$36\ \text{m/s}. $$The police officer accelerates at $$2.00\ \text{m/s}^2. $$How long does it take for the police officer to overtake the speeder?

$$t = \frac{2v_0}{a} = \frac{2 \times 36}{2.00} = 36\ \text{s}$$

Question 1

Which of the following best describes the difference between a vector and a scalar quantity?

Accepted Answer

A vector has both magnitude and direction, while a scalar has only magnitude.

Question 2

A car travels 60 meters east, then 40 meters west. What is the car's total displacement?

Accepted Answer

$$\Delta x = 20\ 	ext{m}\ 	ext{east}$$

Question 3

Which of the following is a vector quantity?

Accepted Answer

Velocity

Question 4

A runner jogs 15 m forward in 2 s, then 9 m backward in another 2 s. What is the average velocity for the total trip?

Accepted Answer

$$v_{avg} = \frac{15\ 	ext{m} - 9\ 	ext{m}}{4\ 	ext{s}} = 1.5\ 	ext{m/s}$$

Question 5

A baseball pitcher throws a ball at 44 m/s toward home plate, which is 18.5 m away. How long does it take for the ball to reach home plate?

Accepted Answer

$$t = \frac{18.5\ 	ext{m}}{44\ 	ext{m/s}} = 0.42\ 	ext{s}$$

Question 6

Which of the following statements about acceleration is correct?

Accepted Answer

Acceleration is always a vector and can be caused by a change in speed or direction.

Question 7

A car accelerates from 5 m/s to 21 m/s at a constant $$3.0\ 	ext{m/s}^2. $$How far does it travel while accelerating?

Accepted Answer

$$\Delta x = \frac{v^2$ - v_0$^2}{2a} = \frac{21^2$ - 5^2$}{2 	imes 3.0} = 68\ 	ext{m}$$

Question 8

On a position-time graph, what does a horizontal (flat) line segment represent?

Accepted Answer

The object is at rest.

Question 9

A moving hockey puck encounters a patch of rough ice and slides 0.90 m before coming to a stop. If the deceleration is $$8.0\ 	ext{m/s}^2$$, what was the puck’s initial speed?

Accepted Answer

$$v_0$$ = \sqrt{2a\Delta x} = \sqrt{2 	imes 8.0 	imes 0.90} = 3.8\ 	ext{m/s}$$

Question 10

Which of the following best describes the area under a velocity-time graph between two points?

Accepted Answer

It represents the displacement $$\Delta x.$$

Question 11

A rock is thrown upward with a speed of $$27.0\ 	ext{m/s}$$ from the roof of a $$31.0\ 	ext{m}$$ tall building. What is the speed of the rock just before it hits the street?

Accepted Answer

$$v = \sqrt{v_0$^2 + 2g\Delta y} = \sqrt{27.0^2$ + 2 	imes 9.8 	imes 31.0} = 36.6\ 	ext{m/s}$$

Question 12

A police car at rest is passed by a speeder traveling at a constant $$36\ 	ext{m/s}. $$The police officer accelerates at $$2.00\ 	ext{m/s}^2. $$How long does it take for the police officer to overtake the speeder?

Accepted Answer

$$t = \frac{2v_0}{a} = \frac{2 	imes 36}{2.00} = 36\ 	ext{s}$$

Question 13

Which of the following is true about the acceleration of an object in free fall near the surface of the Earth (neglecting air resistance)?

Accepted Answer

The acceleration is constant and equal to $$9.8\ 	ext{m/s}^2$$ downward.

Question 14

A student throws a set of keys vertically upward to her friend in a window 14.0 m above. The friend catches the keys 1.50 s later. What was the initial velocity of the keys?

Accepted Answer

$$v_0$$ = \frac{\Delta y + \frac{1}{2}$$gt^2$$}{t} = \frac{14.0 + 0.5 	imes 9.8 	imes $$(1.5)^2$$}{1.5} = 13.9\ 	ext{m/s}$$

Question 15

Which of the following best describes the relationship between the slope of a position-time graph and the motion of an object?

Accepted Answer

The slope represents the velocity of the object.

Question 16

If the velocity-time graph of an object is a straight line with a positive slope, what does this indicate about the object's motion?

Accepted Answer

The object is accelerating at a constant rate.

Question 17

A car is moving to the left at $$30\ 	ext{m/s}$$ and slows down to a stop after traveling $$150\ 	ext{m}. $$What is the magnitude and direction of the acceleration?

Accepted Answer

$$a = \frac{v^2$ - v_0$^2}{2\Delta x} = \frac{0 - (-30)^2$}{2 	imes 150} = -3.0\ 	ext{m/s}^2 (to $$the right)

1D Motion and Kinematics: Foundations and Applications

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