Q: A ball is dropped from a height of 20 m. Neglecting air resistance, what is its velocity just before it hits the ground? (Use $$g = 9.8\ \mathrm{m/s^2$})$$

$$v = \sqrt{2gh} = \sqrt{2 \times 9.8 \times 20} = 19.8\ \mathrm{m/s}$$

Q: A coffee cup is dropped from a height of $$0.8\ \mathrm{m}. $$How long does it take to hit the ground? (Neglect air resistance, $$g = 9.8\ \mathrm{m/s^2$})$$

$$t = \sqrt{\frac{2h}{g}} = \sqrt{\frac{2 \times 0.8}{9.8}} \approx 0.40\ \mathrm{s}$$

Question 1

A car accelerates from rest with a constant acceleration. Which of the following statements about its velocity vs. time graph is correct?

Accepted Answer

The graph is a straight line with a positive slope.

Question 2

Given a velocity vs. time graph with a constant positive slope, what does the slope of this graph represent?

Accepted Answer

The acceleration of the object.

Question 3

A ball is dropped from a height of 20 m. Neglecting air resistance, what is its velocity just before it hits the ground? (Use $$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

$$v = \sqrt{2gh} = \sqrt{2 	imes 9.8 	imes 20} = 19.8\ \mathrm{m/s}$$

Question 4

Which of the following best describes 'free fall' as used in physics?

Accepted Answer

Motion under the influence of gravity only, with no other forces acting.

Question 5

If the position vs. time graph of an object is a parabola opening upwards, what can you say about the acceleration?

Accepted Answer

The acceleration is constant and positive.

Question 6

A coffee cup is dropped from a height of $$0.8\ \mathrm{m}. $$How long does it take to hit the ground? (Neglect air resistance, $$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

$$t = \sqrt{\frac{2h}{g}} = \sqrt{\frac{2 	imes 0.8}{9.8}} \approx 0.40\ \mathrm{s}$$

Question 7

Which of the following is the correct equation for the position $$x of an $$object under constant acceleration $$a$$, starting from initial position $$x_0$$ and initial velocity $$v_0$$?

Accepted Answer

$$x = x_0$ + v_0$ t + \frac{1}{2} a t^2$

Question 8

A velocity vs. time graph for two cars (Corvette and Sonic) shows straight lines with different slopes. What does the difference in slopes indicate?

Accepted Answer

The Corvette has a greater acceleration than the Sonic.

Question 9

Which of the following statements about objects in free fall near Earth's surface is correct?

Accepted Answer

All objects accelerate downward at $$g = 9.8\ \mathrm{m/s^2$}$$ regardless of mass.

Question 10

A student throws a ball straight up with an initial velocity of $$15\ \mathrm{m/s}. $$How long does it take to reach its maximum height? (Use $$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

$$t = \frac{v_0$}{g} = \frac{15}{9.8} \approx 1.53\ \mathrm{s}$$

Question 11

If the slope of a velocity vs. time graph is negative, what does this indicate about the object's motion?

Accepted Answer

The object is experiencing a constant negative acceleration.

Question 12

Which of the following is the correct unit for acceleration?

Accepted Answer

$$\mathrm{m/s^2$}$$

Question 13

A skydiver jumps from a plane and is in free fall before opening the parachute. Which principle explains why the skydiver accelerates downward at $$g$$ before the parachute opens?

Accepted Answer

Gravity is the only force acting on the skydiver.

Question 14

Which of the following is a correct strategy for solving kinematics problems involving free fall?

Accepted Answer

Identify known and unknown variables, choose a coordinate system, and apply the appropriate kinematic equations.

Question 15

A rock is thrown downward from a bridge with an initial velocity of $$5\ \mathrm{m/s}. $$How far does it fall in $$2\ \mathrm{s}$$? (Use $$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

$$d = v_0$ t + \frac{1}{2} g t^2$ = 5 	imes 2 + 0.5 	imes 9.8 	imes 4 = 10 + 19.6 = 29.6\ \mathrm{m}$$

Question 16

Which of the following best describes the relationship between the position vs. time, velocity vs. time, and acceleration vs. time graphs for constant acceleration?

Accepted Answer

The slope of the position vs. time graph gives velocity; the slope of the velocity vs. time graph gives acceleration.

Question 17

A student analyzes a velocity vs. time graph and calculates the slope as $$7.5\ \mathrm{m/s}$$ over a time interval of $$1.0\ \mathrm{s}. $$What is the acceleration?

Accepted Answer

$$a = \frac{\Delta v}{\Delta t} = \frac{7.5}{1.0} = 7.5\ \mathrm{m/s^2$}$$

Question 18

Which of the following is NOT a correct step in the problem-solving strategy for kinematics problems?

Accepted Answer

Assume all objects have the same initial velocity.

Question 19

During the Apollo 15 mission, a hammer and a feather were dropped on the Moon. What did this experiment demonstrate?

Accepted Answer

In the absence of air resistance, all objects fall at the same rate regardless of mass.

Kinematics and Free Fall: Position, Velocity, and Acceleration in Physics 101

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