**Stopping of
Vehicle by Retarding Force**

When the body is moving with a certain velocity and suddenly brakes are applied, then the body stops completely after covering a certain distance, this is called as Stopping Distance. It is the distance travelled between the time when the body decides to stop a moving vehicle and the time when the vehicle stops completely.

If a vehicle moves with some initial velocity and due to some retarding force it stops after covering some distance after some time.

**1) Stopping distance: **

Let, m = Mass of vehicle, \(v\) = Velocity, P = Momentum, K.E = Kinetic Energy, F = Stopping force, x = Stopping distance, t = Stopping time.

Then, in this process stopping force does work on the vehicle and destroy the motion. By the work – energy theorem:

\(W=\Delta K.E=\frac{1}{2}m{{v}^{2}}\)\(\Rightarrow \) Kinetic Energy (K.E) = Stopping force (F) \(\times \) Distance (x)

\(\Rightarrow \) Stopping distance (x) = \(\frac{Kinetic\,\,Energy\left( K.E \right)}{Stopping\,Force\left( F \right)}=\frac{m{{v}^{2}}}{2F}\)

**2) Stopping Time: **

By the impulse – momentum theorem:

\(F\times \Delta t=\Delta P\Rightarrow F\times t=P\) \(\Rightarrow Time\left( t \right)=\frac{P}{F}=\frac{mv}{F}\)