If a vehicle's speed doubles, how does the vehicle's energy change?

When a vehicle's speed doubles, its kinetic energy increases significantly due to the relationship between speed and kinetic energy. Kinetic energy is calculated using the formula:

[ KE = \frac{1}{2}mv^2 ]

where ( m ) represents the mass of the vehicle and ( v ) is its speed. If the speed of the vehicle is doubled, the new speed can be represented as ( 2v ). Plugging this into the kinetic energy formula results in:

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

This demonstrates that when the speed of the vehicle doubles, its kinetic energy quadruples. Therefore, the correct choice indicates that the increase in energy is proportional to the square of the change in speed.