If the vehicle speed is increased by 4 times, how much stopping power is necessary?

When the speed of a vehicle is increased, the amount of stopping power required does not change linearly but instead increases with the square of the speed. This is due to the physics of motion, specifically the kinetic energy formula. Kinetic energy is given by the equation ( KE = \frac{1}{2} mv^2 ), where ( m ) is the mass of the vehicle and ( v ) is its speed.

If the speed is increased by 4 times (i.e., the new speed is ( 4v )), the kinetic energy becomes:

[

KE_{new} = \frac{1}{2} m (4v)^2 = \frac{1}{2} m (16v^2) = 16 \times \frac{1}{2} mv^2 = 16 \times KE_{original}

]

This illustrates that the kinetic energy—and therefore the stopping power necessary to bring the vehicle to a stop—has increased by a factor of 16. Consequently, to safely stop a vehicle travelling at this increased speed, you would require 16 times the original stopping power, making that the correct answer.