If you reduce your speed by half before crashing, how does this affect kinetic energy?

Kinetic energy is calculated using the formula ( KE = \frac{1}{2} mv^2 ), where ( m ) is the mass of the object and ( v ) is its velocity. This formula shows that kinetic energy is directly related to the square of the velocity.

If you reduce your speed by half, you would replace ( v ) in the equation with ( \frac{v}{2} ). When applying this in the kinetic energy formula, you get:

( KE_{new} = \frac{1}{2} m \left(\frac{v}{2}\right)^2 )

When you simplify this, it turns into:

( KE_{new} = \frac{1}{2} m \left(\frac{v^2}{4}\right) = \frac{1}{4} \cdot \frac{1}{2} mv^2 )

This indicates that the new kinetic energy is one-fourth of the original kinetic energy. Thus, by reducing speed by half, the kinetic energy is significantly reduced—specifically, to a quarter of what it was before the reduction in speed. Consequently, the correct response reflects this decrease in kinetic energy when speed is