Q: A 2 kg ball is moving at 3 m/s. What is its kinetic energy?

$$KE = \frac{1}{2}mv^2$ = \frac{1}{2} \times 2 \times 3^2$ = 9\ \text{J}$$

Q: A car of mass 1000 kg is traveling at 20 m/s. What is its kinetic energy?

$$KE = \frac{1}{2} \times 1000 \times 20^2$ = 200,000\ \text{J}$$

Q: A 390 kg bobsled is pushed with a net force of 270 N over a distance of 50 m, starting from rest. Neglecting friction, what is the final speed of the bobsled?

$$v = \sqrt{\frac{2 F d}{m}} = \sqrt{\frac{2 \times 270 \times 50}{390}} \approx 8.3\ \text{m/s}$$

Q: A bullet of mass 0.01 kg is fired at 400 m/s. What is its kinetic energy?

$$KE = \frac{1}{2} \times 0.01 \times 400^2$ = 800\ \text{J}$$

Q: A 0.5 kg ball is dropped from a height and reaches a speed of 6 m/s just before hitting the ground. What is its kinetic energy at that moment?

$$KE = \frac{1}{2} \times 0.5 \times 6^2$ = 9\ \text{J}$$

Question 1

Which of the following statements about kinetic energy is correct?

Accepted Answer

Kinetic energy is always positive for moving objects and zero for objects at rest.

Question 2

A 2 kg ball is moving at 3 m/s. What is its kinetic energy?

Accepted Answer

$$KE = \frac{1}{2}mv^2$ = \frac{1}{2} 	imes 2 	imes 3^2$ = 9\ 	ext{J}$$

Question 3

If the mass of an object is doubled while its velocity remains constant, what happens to its kinetic energy?

Accepted Answer

The kinetic energy is doubled.

Question 4

A 1 kg object is moving at 5 m/s. If its velocity is doubled, what is its new kinetic energy compared to the original?

Accepted Answer

It is quadrupled.

Question 5

Which would require more energy to stop: a 5 kg cat running at 10 m/s or a 5000 kg elephant running at 2 m/s?

Accepted Answer

The elephant, because its mass is much greater.

Question 6

A car of mass 1000 kg is traveling at 20 m/s. What is its kinetic energy?

Accepted Answer

$$KE = \frac{1}{2} 	imes 1000 	imes 20^2$ = 200,000\ 	ext{J}$$

Question 7

A 390 kg bobsled is pushed with a net force of 270 N over a distance of 50 m, starting from rest. Neglecting friction, what is the final speed of the bobsled?

Accepted Answer

$$v = \sqrt{\frac{2 F d}{m}} = \sqrt{\frac{2 	imes 270 	imes 50}{390}} \approx 8.3\ 	ext{m/s}$$

Question 8

Which of the following best explains why doubling the velocity of an object increases its kinetic energy by a factor of four?

Accepted Answer

Because kinetic energy is directly proportional to the square of velocity: $$KE = \frac{1}{2}mv^2$

Question 9

A bullet of mass 0.01 kg is fired at 400 m/s. What is its kinetic energy?

Accepted Answer

$$KE = \frac{1}{2} 	imes 0.01 	imes 400^2$ = 800\ 	ext{J}$$

Question 10

Which of the following scenarios would result in the greatest increase in kinetic energy?

Accepted Answer

Doubling the velocity of a moving object.

Question 11

A cyclist and bicycle together have a mass of 80 kg and are moving at 10 m/s. If the cyclist increases speed to 20 m/s, by what factor does the kinetic energy increase?

Accepted Answer

By a factor of 4

Question 12

A 0.5 kg ball is dropped from a height and reaches a speed of 6 m/s just before hitting the ground. What is its kinetic energy at that moment?

Accepted Answer

$$KE = \frac{1}{2} 	imes 0.5 	imes 6^2$ = 9\ 	ext{J}$$

Question 13

Which of the following is NOT a correct property of kinetic energy?

Accepted Answer

Kinetic energy can be negative if the object is moving backwards.

Question 14

A 70 kg person is running at 5 m/s. How much kinetic energy do they have?

Accepted Answer

$$KE = \frac{1}{2} 	imes 70 	imes 5^2$ = 875\ 	ext{J}$$

Question 15

A coin of mass 0.02 kg is dropped from a height and reaches a speed of 2 m/s just before hitting the ground. What is its kinetic energy?

Accepted Answer

$$KE = \frac{1}{2} 	imes 0.02 	imes 2^2$ = 0.04\ 	ext{J}$$

Question 16

If a car's kinetic energy increases from 50,000 J to 200,000 J, by what factor did its speed increase?

Accepted Answer

By a factor of 2, since $$KE \propto v^2$, $$\sqrt{200,000/50,000} = 2$$

Question 17

A 10 kg bowling ball is rolled at 4 m/s. If the same ball is rolled at 8 m/s, how does its kinetic energy compare to the original?

Accepted Answer

It is four times as much.

Question 18

Which of the following real-world examples best illustrates the concept that kinetic energy depends more strongly on velocity than mass?

Accepted Answer

A small bullet fired at high speed causing more damage than a slow-moving heavy truck.

Kinetic Energy: Concepts, Calculations, and Applications

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