Question

A car and a truck moving with the same velocity in opposite directions collide and collision lasts for `2 s`.
(i) Which vehicle experiences the greater force of impact?
(ii) Which vehicle has the smaller change in momentum?
(iii) Which one undergoes greater acceleration?
(iv) Which one is pushed farther?
(v) Which one is likely to suffer more damage?

Answer 1

Let mass of truck `=M`, mass of car `=m`
velocity of truck `=v`
velocity of car `= -v` (Negative sign for opposite direction of motion)
time for which collision lasts, `t=1s`
(a) On collision, both the vehicles experience the same force, as action and reaction are equal.
(b) Change in momentum of truck is equal and opposite to change in momentum of car, i.e., both the vehicles experience the same change in momentum.
(c) As acceleration=force/mass, and force on each vehicle in same, therefore, acceleration `prop1/("mass")`
As mass of car is smaller, therefore, acceleration of car is greater than the acceleration of the truck.
(d) The car is likely to suffer more damage than the truck, as it is lighter. The acceleration, i.e., change in velocity of car is more than of the truck.