How is kinetic energy affected when traveling at twice the speed?

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 an object doubles, you can see the effect on kinetic energy by substituting ( 2v ) into the equation.

If you replace ( v ) with ( 2v ), the new kinetic energy becomes:

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

This shows that the new kinetic energy is four times the original kinetic energy because the velocity is squared in the kinetic energy formula. Thus, when traveling at twice the speed, the kinetic energy increases by a factor of four, which is why this option is correct.