Why doubling a car speed have much bigger impact on it kinetic energy that doubling it mass

The formula for kinetic energy is:

$$KE = \frac{1}{2}mv^2$$

where $m$ is mass and $v$ is speed (velocity).

• If you double the mass ($2m$), the kinetic energy becomes $KE = \frac{1}{2}(2m)v^2 = 2 \times (\frac{1}{2}mv^2)$, which is twice the original kinetic energy.
• If you double the speed ($2v$), the kinetic energy becomes $KE = \frac{1}{2}m(2v)^2 = \frac{1}{2}m(4v^2) = 4 \times (\frac{1}{2}mv^2)$, which is four times the original kinetic energy.

Therefore, because speed is squared in the kinetic energy formula, changes in speed have a much more significant effect on kinetic energy than equivalent changes in mass.