Question

A car and a lorry are moving with the same momentum. If same brake force is applied then,
A) car comes to rest in short distance
B) lorry comes to rest in short distance
C) both travels the same distance before coming to rest
D) insufficient data

Answer 1

Hint: To solve this question, we have to understand the concept of momentum. The momentum is defined as a product of mass and velocity. In this question, we have to consider the momentum as the combined effect of mass and velocity to solve this question. Complete step-by-step answer:The momentum is defined as the product of mass and the velocity of the body. Momentum, $p = mv$
where m = mass and v = velocity.
However, this is only the mathematical definition. The momentum of a body represents the effect or impact that it possesses by the virtue of its mass and the velocity at which it is moving. We can understand that momentum represents the consequence of the body moving.
Consider a car and a lorry moving with the same momentum p. When the brakes are applied, force is applied on the vehicles to stop their motion.
Force is defined as the rate of change of momentum per unit time. Thus, when force is applied on the vehicles, their momentum is reduced to zero, thereby making them stop.
If we consider momentum of the car and the lorry to be same, we have –
$p = mv$
$m \propto \dfrac{1}{v}$
This expression states that the mass of the object is inversely proportional to the velocity if the momentum remains constant.
When the brakes are applied, and the momentum of the car and the lorry are reduced to zero eventually, the one with the higher mass moves a smaller velocity and conversely, the one with the lower mass moves with a larger velocity. This is based on the relation derived above, that the mass is inversely proportional to the velocity when the momentum is the same.
Since, the car has less mass than lorry, the lorry moves a smaller distance before coming to rest at lesser velocity compared to the car, which moves faster and stops at a larger distance.

Hence, the correct option is Option B.

Note: When the car and the truck are moving at the same velocity, the impact produced by the lorry is higher than that of the car owing to its higher mass. This matters during collisions when we have the question as to whether lorry or the car suffers greater damage after colliding with a similar object. The lorry suffers a greater damage given its high momentum.