If the velocity of an object doubles, what happens to its kinetic energy?

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Question: If the velocity of an object doubles, what happens to its kinetic energy?

Options:

Correct Answer: It quadruples

Solution:

Kinetic energy (KE) is given by KE = 1/2 mv². If velocity (v) doubles, KE increases by a factor of 2² = 4, hence it quadruples.

If the velocity of an object doubles, what happens to its kinetic energy?

If the velocity of an object doubles, what happens to its kinetic energy?

Step 1: Understand the formula for kinetic energy, which is KE = 1/2 mv², where m is mass and v is velocity.
Step 2: Identify what happens when the velocity (v) of the object doubles. If v becomes 2v, we need to substitute this into the formula.
Step 3: Substitute the new velocity into the kinetic energy formula: KE = 1/2 m(2v)².
Step 4: Calculate (2v)², which equals 4v².
Step 5: Now the kinetic energy formula looks like this: KE = 1/2 m(4v²).
Step 6: Simplify the equation: KE = 2 mv², which is 4 times the original kinetic energy (since the original KE was 1/2 mv²).
Step 7: Conclude that when the velocity doubles, the kinetic energy increases by a factor of 4.

Kinetic Energy – Kinetic energy is the energy an object possesses due to its motion, calculated using the formula KE = 1/2 mv², where m is mass and v is velocity.
Effect of Velocity on Kinetic Energy – Kinetic energy is proportional to the square of the velocity, meaning that if velocity doubles, kinetic energy increases by a factor of four.