Why does doubling a vehicle speed increase it kinetic energy much more than doubling it mass refer to kinetic energy fomule in your response

The kinetic energy formula is:

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

where:

• $KE$ is kinetic energy
• $m$ is mass
• $v$ is velocity (speed)

If you double the mass ($2m$) while keeping velocity constant, the new kinetic energy is:

$$KE_{new, mass} = \frac{1}{2}(2m)v^2 = 2 \left(\frac{1}{2}mv^2\right) = 2 \times KE$$

So, doubling the mass doubles the kinetic energy.

If you double the velocity ($2v$) while keeping mass constant, the new kinetic energy is:

$$KE_{new, speed} = \frac{1}{2}m(2v)^2 = \frac{1}{2}m(4v^2) = 4 \left(\frac{1}{2}mv^2\right) = 4 \times KE$$

So, doubling the speed quadruples the kinetic energy.

Because velocity is squared in the formula, changes in speed have a much greater impact on kinetic energy than equivalent changes in mass.