Question

A lorry and a car moving with the same K.E. are given the same retarding force, then
A. The lorry will come to rest in a shorter distance.
B. The car will come to rest in a shorter distance
C. Both come to rest at the same distance
D. None of these

Answer 1

A retarding force always tends to bring a body in motion to rest.
Kinetic energy is the energy possessed by an object due to its motion. It is the work needed to accelerate a body of given mass from rest to its required velocity, and the body will move unless its speed changes. This can be formulated as$K.E = \dfrac{1}{2}m{\left( v \right)^2}$, where m is the mass, and v is the velocity of the object.
A resistive force or the retarding force is a force whose direction is always opposite to the direction of the velocity of the body, and it tends to bring an object to the rest.

Complete step by step answer: Both the vehicle lorry and the car are moving with the same Kinetic Energy, and they are given the same retarding force.
We know when a brake is applied in a vehicle, it comes to rest after traveling some distance, and this distance differs by the amount of retarding force.
Now since both the vehicles are moving with the same Kinetic Energy and also, they are given the same retarding force, hence we can say
The kinetic energy of vehicle = Retarding Force (F)
This can be formulated as $K.E = W = F.S$
We can write this as
$S = \dfrac{{K.E}}{F}$
Now since $K.E$and $F$ are the same for both the cars and the lorry then both the vehicle comes to rest in the same distance.
Option (C) is correct.

Note: Students must note when the retarding force applies to a car is less than its kinetic speed, then the vehicle will cover more distance after applying the brakes.