If the speed of an object doubles, how does its kinetic energy change?

Kinetic energy is given by the formula ( KE = \frac{1}{2} mv^2 ), where ( m ) is the mass of the object and ( v ) is its velocity. When the speed of the object doubles, it means the new velocity ( v' ) is ( 2v ).

Substituting this new velocity into the kinetic energy formula gives:

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

This shows that the new kinetic energy is four times the original kinetic energy, confirming that when the speed doubles, the kinetic energy is indeed quadrupled. Therefore, the correct answer accurately reflects the relationship between speed and kinetic energy; as speed increases, kinetic energy increases by the square of that change in speed.