Work, Energy and Power — Question 11

Let speed of car be v.

Kinetic Energy at speed v = $\dfrac{1}{2}$ x m x v² = $\dfrac{\text{mv}^2}{2}$

Kinetic Energy at speed $\dfrac{\text{v}}{2}$ = $\dfrac{1}{2}$ x m x $(\dfrac{\text{v}}{2})^2$ = $\dfrac{\text{mv}^2}{8}$ = $\dfrac{1}{4}\Big(\dfrac{\text{mv}^2}{2}\Big)$

Hence, when the speed of the car is halved the kinetic energy becomes one-fourth.