What happens to kinetic energy if the velocity of an object doubles?

• A. Kinetic energy increases by a factor of four
• B. Kinetic energy remains the same
• C. Kinetic energy increases by a factor of two
• D. Kinetic energy becomes negligible

Answer: (A)

Kinetic energy is defined by the formula ( KE = \frac{1}{2} mv^2 ), where ( m ) is the mass of the object and ( v ) is its velocity. When the velocity of an object doubles, the new velocity can be represented as ( 2v ). Substituting this into the kinetic energy formula gives:

[

KE' = \frac{1}{2} m (2v)^2 = \frac{1}{2} m (4v^2) = 2mv^2

]

This shows that the new kinetic energy ( KE' ) is four times the original kinetic energy ( KE ), as the original ( KE = \frac{1}{2} mv^2 ).

Thus, when velocity is doubled, kinetic energy increases by a factor of four. This relationship highlights the power of the velocity term in the kinetic energy equation, as it is squared. Therefore, the correct choice is that kinetic energy increases by a factor of four.