Q: A car travels 40 km east and then 30 km west. What is the car's displacement?

$$10 \ \text{km}$$ \ \text{east}$

Q: If a ball is dropped from a height of 20 m, what is its velocity just before hitting the ground? (Assume $$g = 9.81 \ \text{m/s}^2$$ and neglect air resistance.)

$$v = \sqrt{2gh} = \sqrt{2 \times 9.81 \times 20} \approx 19.8 \ \text{m/s}$$

Q: Which of the following is a correct unit conversion for speed?

$$1 \ \text{km/h} = 0.2778 \ \text{m/s}$$

Q: What is the mechanical energy of a 2 kg object at a height of 5 m moving at 3 m/s? (Use $$g = 9.81 \ \text{m/s}^2)$$

$$E = mgh + \frac{1}{2}mv^2$ = 2 \times 9.81 \times 5 + \frac{1}{2} \times 2 \times 3^2$ = 98.1 + 9 = 107.1 \ \text{J}$$

Q: A pendulum is released from a height of 0.5 m. What is its potential energy at the highest point? (Mass = 0.2 kg, $$g = 9.81 \ \text{m/s}^2)$$

$$E_p = mgh = 0.2 \times 9.81 \times 0.5 = 0.981 \ \text{J}$$

Q: Which formula is used to calculate percent efficiency in an energy conversion process?

$$\text{percent efficiency} = \frac{\text{useful output}}{\text{input}} \times 100\%$$

Q: A 5 kg object is moving at 4 m/s. What is its kinetic energy?

$$E_k = \frac{1}{2}mv^2$ = \frac{1}{2} \times 5 \times 4^2$ = 40 \ \text{J}$$

Question 1

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

Accepted Answer

Distance is the total length traveled, while displacement is the straight-line change in position.

Question 2

A car travels 40 km east and then 30 km west. What is the car's displacement?

Accepted Answer

$$10 \ 	ext{km}$$ \ 	ext{east}$

Question 3

Which equation correctly relates force, mass, and acceleration?

Accepted Answer

$$F = m a$$

Question 4

If a ball is dropped from a height of 20 m, what is its velocity just before hitting the ground? (Assume $$g = 9.81 \ 	ext{m/s}^2$$ and neglect air resistance.)

Accepted Answer

$$v = \sqrt{2gh} = \sqrt{2 	imes 9.81 	imes 20} \approx 19.8 \ 	ext{m/s}$$

Question 5

Which of the following is a correct unit conversion for speed?

Accepted Answer

$$1 \ 	ext{km/h} = 0.2778 \ 	ext{m/s}$$

Question 6

A student calculates the area of a rectangle as $$3.45 \ 	ext{m} 	imes 2.1 \ 	ext{m}. $$How many significant digits should the answer have?

Accepted Answer

2

Question 7

Which graph best represents an object moving with constant acceleration?

Accepted Answer

A straight line on a velocity vs. time graph

Question 8

What is the mechanical energy of a 2 kg object at a height of 5 m moving at 3 m/s? (Use $$g = 9.81 \ 	ext{m/s}^2)$$

Accepted Answer

$$E = mgh + \frac{1}{2}mv^2$ = 2 	imes 9.81 	imes 5 + \frac{1}{2} 	imes 2 	imes 3^2$ = 98.1 + 9 = 107.1 \ 	ext{J}$$

Question 9

Which of the following statements about the Law of Conservation of Energy is correct?

Accepted Answer

Energy can only be transferred or transformed, not created or destroyed.

Question 10

A pendulum is released from a height of 0.5 m. What is its potential energy at the highest point? (Mass = 0.2 kg, $$g = 9.81 \ 	ext{m/s}^2)$$

Accepted Answer

$$E_p = mgh = 0.2 	imes 9.81 	imes 0.5 = 0.981 \ 	ext{J}$$

Question 11

Which formula is used to calculate percent efficiency in an energy conversion process?

Accepted Answer

$$	ext{percent efficiency} = \frac{	ext{useful output}}{	ext{input}} 	imes 100\%$$

Question 12

A 5 kg object is moving at 4 m/s. What is its kinetic energy?

Accepted Answer

$$E_k = \frac{1}{2}mv^2$ = \frac{1}{2} 	imes 5 	imes 4^2$ = 40 \ 	ext{J}$$

Question 13

Which of the following is NOT a type of potential energy?

Accepted Answer

Thermal

Question 14

A box is pushed with a force of 10 N over a distance of 3 m. How much work is done?

Accepted Answer

$$W = Fd = 10 	imes 3 = 30 \ 	ext{J}$$

Question 15

Which of the following best describes a scalar quantity?

Accepted Answer

A quantity with only magnitude

Question 16

If a runner accelerates from rest to 8 m/s in 4 seconds, what is their acceleration?

Accepted Answer

$$a = \frac{v_f - v_i}{t} = \frac{8 - 0}{4} = 2 \ 	ext{m/s}^2$$

Question 17

Which of the following is the correct rearrangement to solve for mass in the kinetic energy equation $$E_k = \frac{1}{2}mv^2$?

Accepted Answer

$$m = \frac{2E_k}{v^2$}$$

Question 18

A cyclist increases their speed from 5 m/s to 15 m/s. What is the change in kinetic energy if the mass of the cyclist and bike is 70 kg?

Accepted Answer

$$\Delta E_k = \frac{1}{2}m(v_f^2$ - v_i^2$) = \frac{1}{2} 	imes 70 	imes (225 - 25) = 35 	imes 200 = 7000 \ 	ext{J}$$

Key Concepts for Physics: Units, Kinematics, Work, and Energy

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