A large truck and a car, both moving with a velocity of magnitude *v*, have a head-on collision and both of them come to a halt after that. If the collision lasts for 1 s:-

(a) Which vehicle experiences the greater force of impact?

(b) Which vehicle experiences the greater change in momentum?

(c) Which vehicle experiences the greater acceleration?

(d)Why is the car likely to suffer more damage than the truck?

#### Solution

Let the mass of the truck be *M* and that of the car be *m*.

Thus, *M* > *m*

Initial velocity of both vehicles, *v*

Final velocity of both vehicles, *v*’ = 0 (since the vehicles come to rest after collision)

Time of impact, *t* = 1 s

(a) From Newton’s second law of motion, the net force experienced by each vehicle is given by the relation:-

`F_(car)=(m(v'-v))/t=-mv`

`F_(truck)=(M(v'-v))/t=-Mv`

Since the mass of the truck is greater than that of the car, it will experience a greater force of impact.

(b) Initial momentum of the car = *mv*

Final momentum of the car = 0

Change in momentum = *mv*

Initial momentum of the truck = *Mv*

Final momentum of the truck = 0

Change in momentum = *Mv*

Since the mass of the truck is greater than that of the car, it will experience a greater change in momentum.

(c) From the first equation of motion, acceleration produced in a system is independent of the mass of the system. The initial velocity, the final velocity, and the time of impact remain the same in both cases. Hence, both the car and the truck experience the same amount of acceleration.

(d)According to Newton’s third law of motion, for every action there is an equal and opposite reaction that acts on different bodies. Since the truck experiences a greater force of impact (action), this larger impact force is also experienced by the car (reaction). Thus, the car is likely to suffer more damage than the truck.