Free Kinetic Energy MCQs with Answers

1. The kinetic energy of a body is doubled when its

• A. mass is halved
• B. speed is doubled
• C. speed is increased by a factor of the square root of two
• D. mass is doubled and speed halved

Explanation: Kinetic energy is half m v squared, so it scales with the square of the speed. Multiplying the speed by root 2 multiplies the energy by 2, whereas doubling the speed multiplies the energy by 4. The last option leaves energy at half its original value, since doubling m and quartering v squared gives a net factor of one half.

2. A body of mass 5 kg moves at 4 m s-1. Its kinetic energy is

• A. 10 J
• B. 20 J
• C. 40 J
• D. 80 J

Explanation: Kinetic energy is half times 5 times 4 squared, which is half times 5 times 16, giving 40 J. The common slip is to forget to square the velocity, which gives 10 J, or to forget the factor of one half, which gives 80 J.

3. The kinetic energy of a body of mass m moving with speed v is

• A. mv
• B. half mv squared
• C. mv squared
• D. half mv

Explanation: Because the speed is squared, doubling it quadruples the kinetic energy, which is why stopping distances grow so sharply with speed. Momentum, by contrast, is mv and only doubles. The factor of one half comes from integrating the force over the distance during acceleration from rest.

4. If the speed of a car is doubled, its kinetic energy becomes

• A. double
• B. four times
• C. half
• D. unchanged

Explanation: Kinetic energy depends on the square of the speed, so a factor of two in speed gives a factor of four in energy, and the braking distance rises in the same proportion since the brakes must dissipate all of it. This is the physics behind speed limits. The momentum, meanwhile, only doubles.

5. A body of mass 1 kg has kinetic energy 50 J. Its speed is

• A. 5 m per second
• B. 10 m per second
• C. 50 m per second
• D. 100 m per second

Explanation: From half mv squared equal to 50, v squared is 100 and v is 10 m per second. Forgetting the factor of one half gives about 7.1, and forgetting to take the square root gives 100. Checking the units at the end is a quick guard against both slips.

6. If P is the momentum of an object and m is its mass, then its kinetic energy is:

• A. P/2m
• B. P2/2m
• C. 1/2 Pm2
• D. 1/2 P2m

Explanation: Kinetic energy is half mv squared and momentum is mv, so substituting v equal to P over m gives half m multiplied by P squared over m squared, which simplifies to P squared over 2m. A quick check is that energy must rise with the square of momentum, which only the second option does. This relation is used constantly in collision and de Broglie problems.

7. A 0.5 kg ball moving at 6 m/s has kinetic energy

• A. 9 J
• B. 18 J
• C. 6 J
• D. 3 J

Explanation: Kinetic energy is half mv squared, so half multiplied by 0.5 multiplied by 36 gives 9 J. Forgetting the factor of one half gives 18 J, which is the commonest slip. Note that the momentum of the same ball would be 3 kg m per second, which is why 3 also appears as a distractor.