Q: A car travels 150 km in 3 hours, but its speed varies throughout the trip. What is the car's average speed?

$$\frac{150\ \text{km}}{3\ \text{h}} = 50\ \text{km/h}$$

Q: A ball is dropped from rest and falls freely under gravity. What is its velocity after $$3\ \text{s}$$? (Use $$g = 10\ \text{m/s}^2)$$

$$v = gt = 10\ \text{m/s}^2 \times 3\ \text{s} = 30\ \text{m/s}$$

Q: A car accelerates from $$0 to$$ $$20\ \text{m/s} in$$ $$4\ \text{s}. $$What is its acceleration?

$$a = \frac{\Delta v}{\Delta t} = \frac{20\ \text{m/s} - 0}{4\ \text{s}} = 5\ \text{m/s}^2$$

Q: A ball thrown straight upward with an initial speed of $$30\ \text{m/s}. $$How long does it take to reach its highest point? (Use $$g = 10\ \text{m/s}^2)$$

$$t = \frac{v}{g} = \frac{30\ \text{m/s}}{10\ \text{m/s}^2} = 3\ \text{s}$$

Q: A skydiver falls freely for $$2\ \text{s}$$ before opening the parachute. What distance does the skydiver fall during this time? (Use $$g = 10\ \text{m/s}^2)$$

$$d = \frac{1}{2}gt^2$ = \frac{1}{2} \times 10\ \text{m/s}^2 \times (2\ \text{s})^2$ = 20\ \text{m}$$

Q: An airplane flies east at $$120\ \text{km/h}$$ while a crosswind blows north at $$90\ \text{km/h}. $$What is the airplane's resultant speed relative to the ground?

$$v_{\text{resultant}} = \sqrt{120^2$ + 90^2$} = \sqrt{14400 + 8100} = \sqrt{22500} = 150\ \text{km/h}$$

Q: A swimmer swims directly across a river at $$4\ \text{m/s}$$ while the river flows at $$4\ \text{m/s}$$ perpendicular to the swimmer's motion. What is the swimmer's speed relative to the shore?

$$v_{\text{resultant}} = \sqrt{4^2$ + 4^2$} = \sqrt{16 + 16} = \sqrt{32} \approx 5.7\ \text{m/s}$$

Q: A car moves at $$80\ \text{km/h}$$ relative to the ground. What is its speed relative to the Sun, given that Earth moves at $$30\ \text{km/s}$$ relative to the Sun?

Approximately $$30\ \text{km/s}$$, since the car's speed is negligible compared to Earth's speed.

Question 1

A car travels 150 km in 3 hours, but its speed varies throughout the trip. What is the car's average speed?

Accepted Answer

$$\frac{150\ 	ext{km}}{3\ 	ext{h}} = 50\ 	ext{km/h}$$

Question 2

Which of the following statements best describes the difference between speed and velocity?

Accepted Answer

Speed is a scalar quantity; velocity is a vector quantity.

Question 3

A runner moves at a constant speed of $$8\ 	ext{m/s}$$ around a circular track. Which statement is true about the runner's velocity and acceleration?

Accepted Answer

Velocity is changing due to direction; acceleration is nonzero.

Question 4

A ball is dropped from rest and falls freely under gravity. What is its velocity after $$3\ 	ext{s}$$? (Use $$g = 10\ 	ext{m/s}^2)$$

Accepted Answer

$$v = gt = 10\ 	ext{m/s}^2 	imes 3\ 	ext{s} = 30\ 	ext{m/s}$$

Question 5

A car accelerates from $$0 to$$ $$20\ 	ext{m/s} in$$ $$4\ 	ext{s}. $$What is its acceleration?

Accepted Answer

$$a = \frac{\Delta v}{\Delta t} = \frac{20\ 	ext{m/s} - 0}{4\ 	ext{s}} = 5\ 	ext{m/s}^2$$

Question 6

A ball thrown straight upward with an initial speed of $$30\ 	ext{m/s}. $$How long does it take to reach its highest point? (Use $$g = 10\ 	ext{m/s}^2)$$

Accepted Answer

$$t = \frac{v}{g} = \frac{30\ 	ext{m/s}}{10\ 	ext{m/s}^2} = 3\ 	ext{s}$$

Question 7

A skydiver falls freely for $$2\ 	ext{s}$$ before opening the parachute. What distance does the skydiver fall during this time? (Use $$g = 10\ 	ext{m/s}^2)$$

Accepted Answer

$$d = \frac{1}{2}gt^2$ = \frac{1}{2} 	imes 10\ 	ext{m/s}^2 	imes (2\ 	ext{s})^2$ = 20\ 	ext{m}$$

Question 8

An airplane flies east at $$120\ 	ext{km/h}$$ while a crosswind blows north at $$90\ 	ext{km/h}. $$What is the airplane's resultant speed relative to the ground?

Accepted Answer

$$v_{	ext{resultant}} = \sqrt{120^2$ + 90^2$} = \sqrt{14400 + 8100} = \sqrt{22500} = 150\ 	ext{km/h}$$

Question 9

A swimmer swims directly across a river at $$4\ 	ext{m/s}$$ while the river flows at $$4\ 	ext{m/s}$$ perpendicular to the swimmer's motion. What is the swimmer's speed relative to the shore?

Accepted Answer

$$v_{	ext{resultant}} = \sqrt{4^2$ + 4^2$} = \sqrt{16 + 16} = \sqrt{32} \approx 5.7\ 	ext{m/s}$$

Question 10

A car moves at $$80\ 	ext{km/h}$$ relative to the ground. What is its speed relative to the Sun, given that Earth moves at $$30\ 	ext{km/s}$$ relative to the Sun?

Accepted Answer

Approximately $$30\ 	ext{km/s}$$, since the car's speed is negligible compared to Earth's speed.

Question 11

Which car control causes acceleration by changing the direction of motion?

Accepted Answer

Steering wheel

Question 12

A ball rolling down an incline gains $$2\ 	ext{m/s} of $$speed every second. What is its acceleration?

Accepted Answer

$$a = 2\ 	ext{m/s}^2$$

Question 13

If an object moves at a constant velocity, which statement is true?

Accepted Answer

Its acceleration is zero.

Question 14

A jumper achieves a vertical leap of $$1.25\ 	ext{m}. $$What is the total hang time? (Use $$g = 10\ 	ext{m/s}^2)$$

Accepted Answer

$$t = \sqrt{\frac{2d}{g}} = \sqrt{\frac{2 	imes 1.25}{10}} = \sqrt{0.25} = 0.5\ 	ext{s} (up$$), so total hang time $$= 1\ 	ext{s}$$

Question 15

Which scenario best illustrates acceleration due to a change in direction, not speed?

Accepted Answer

A car turning at constant speed around a curve.

Question 16

A ball is thrown upward and returns to its original height. At the same height, how do the magnitudes of its upward and downward velocities compare?

Accepted Answer

They are equal in magnitude but opposite in direction.

Question 17

Which of the following is NOT a way an object can accelerate?

Accepted Answer

Maintaining constant speed and direction.

Question 18

A car moves at $$400\ 	ext{km/h} in a $$straight line. What is its acceleration?

Accepted Answer

Zero, since velocity is constant.

Question 19

If acceleration acts opposite to velocity, what happens to the object?

Accepted Answer

It slows down.

Question 20

A car travels east at $$60\ 	ext{km/h}$$ and another car travels west at $$60\ 	ext{km/h}. $$What is true about their velocities?

Accepted Answer

They have equal magnitudes but opposite directions.

Linear Motion: Speed, Velocity, and Acceleration (Chapter 3)

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