91Ó°ÊÓ

If the final speed of a body becomes zero from a certain speed, then the distance traveled in this duration is known as the stopping distance.

The stopping distance depends on the kinetic energy of the body; it gets affected by the change in speed.

The relation of the kinetic energy of the car is given by:

\(KE = \frac{1}{2}m{v^2}\)

Here, m is the mass of the car, and v is the speed of the car.

In the case of constant stopping force, the stopping distance relies on the initial kinetic energy of the car because the final kinetic energy will be zero as speed becomes zero.

It is known that the kinetic energy rises with the square of the speed. So, if the value of speed changes from v to 2v, the stopping distance becomes four times (4d) from d.

Mathematically it can be expressed as follows:

Work is defined as the change in kinetic energy. Therefore,

\(\begin{aligned}W &= \frac{1}{2}m{v^2} - 0\\Fd &= \frac{1}{2}m{v^2}\\d \propto {v^2}\end{aligned}\)

Here, W is work done, F is the constant force, and d is the stopping distance.

Thus, option (d) is the correct answer.