Stopping of Vehicle by Retarding Force.

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,  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

 Stopping force (F) ´ Distance (x) = Kinetic energy (E)

=>  Stopping distance (x) =Kinetic Energy(E) / Stopping Force(F)

 

Stopping time : By the impulse-momentum theorem

                                   F * t = Δp

                            t=p/F

or                                         =mv/F