Q: A ball is thrown straight up with an initial velocity of $$10 m/s. $$Ignoring air resistance, what is the maximum height reached by the ball? (Use $$g = 9.8 m/s$^2)$$

$$h = \frac{v_0$^2}{2g} = \frac{(10)^2$}{2 \times 9.8} \approx 5.1 m$$

Question 1

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

Accepted Answer

Distance is a scalar quantity representing the total path length traveled, while displacement is a vector quantity representing the straight-line change in position from the initial to the final point.

Question 2

A runner completes one full lap around a 400 m circular track, starting and ending at the same point. What is the runner's displacement and distance traveled?

Accepted Answer

Displacement = $$0 m$$, Distance = $$400 m$$

Question 3

Which of the following is the correct formula for average velocity?

Accepted Answer

$$v_{avg} = \frac{\Delta x}{\Delta t}$$

Question 4

A car travels east for 60 km in 1 hour, then west for 40 km in 0.5 hours. What is the car's average speed and average velocity for the entire trip?

Accepted Answer

Average speed = $$80 km$$ / $$1.5 h$$ $$= 53.3 km/h$$; Average velocity = $$20 km $$east / $$1.5 h$$ $$= 13.3 km/h $$east

Question 5

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

Accepted Answer

Velocity is a vector quantity and can be negative, while speed is a scalar and always positive.

Question 6

A cyclist moves with a constant velocity of $$5 m/s $$east for $$10$$ seconds. What is the displacement of the cyclist?

Accepted Answer

$$50 m $$east

Question 7

Which of the following best describes acceleration?

Accepted Answer

The rate of change of velocity with respect to time.

Question 8

A car accelerates uniformly from rest to $$20 m/s in$$ $$5$$ seconds. What is its acceleration?

Accepted Answer

$$a = \frac{20\ \mathrm{m/s} - 0\ \mathrm{m/s}}{5\ \mathrm{s}} = 4\ \mathrm{m/s}^2$$

Question 9

Which of the following is the correct kinematic equation for displacement when acceleration is constant?

Accepted Answer

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

Question 10

A ball is thrown straight up with an initial velocity of $$10 m/s. $$Ignoring air resistance, what is the maximum height reached by the ball? (Use $$g = 9.8 m/s$^2)$$

Accepted Answer

$$h = \frac{v_0$^2}{2g} = \frac{(10)^2$}{2 	imes 9.8} \approx 5.1 m$$

Question 11

Which of the following best describes the meaning of a negative acceleration?

Accepted Answer

The velocity is decreasing in the direction of motion.

Question 12

A car moves with a velocity of $$15 m/s $$for $$4$$ seconds, then accelerates at $$2 m/s$^2$$ for $$3$$ seconds. What is the car's final velocity?

Accepted Answer

$$v = v_0$ + a t = 15 + 2 	imes 3 = 21 m/s$$

Question 13

Which of the following is NOT a vector quantity?

Accepted Answer

Speed

Question 14

A train travels $$120 km $$north in $$2$$ hours, then $$60 km $$south in $$1$$ hour. What is the train's average velocity?

Accepted Answer

$$\frac{120 - 60}{3} = 20 km/h $$north

Question 15

Which of the following statements about instantaneous velocity is correct?

Accepted Answer

It is the velocity of an object at a specific instant in time.

Question 16

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 with constant positive velocity.

Question 17

A car starts from rest and accelerates uniformly at $$3 m/s$^2$$ for $$6$$ seconds. What is the distance covered by the car?

Accepted Answer

$$\Delta x = \frac{1}{2} a t^2$ = \frac{1}{2} 	imes 3 	imes 36 = 54 m$$

Question 18

Which of the following is the correct definition of a scalar quantity?

Accepted Answer

A quantity that has magnitude only and no direction.

Question 19

A student walks $$3 m $$east, then $$4 m $$north. What is the magnitude of the student's displacement?

Accepted Answer

$$\sqrt{3^2$ + 4^2$} = 5 m$$

Question 20

Which of the following best describes uniform motion?

Accepted Answer

Motion with constant velocity.

Kinematics: Motion in One Dimension

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