$A$ large truck and a car,both moving with speed $v$,have a head-on collision and both of them come to a halt after that. If the collision lasts for $10 \ s$:
$(i)$ Which vehicle experiences the greater force of impact?
$(ii)$ Which vehicle experiences the greater momentum change?
$(iii)$ Which vehicle experiences the greater acceleration?
$(iv)$ Why is the car likely to suffer more damage than the truck?

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(N/A) $(i)$ Both vehicles experience the same force of impact because action and reaction are equal and opposite (Newton's Third Law).
$(ii)$ The truck experiences a greater change in momentum because momentum change $\Delta p = m \Delta v$. Since the truck has a much larger mass $(M > m)$,the change in momentum is greater for the truck.
$(iii)$ The car experiences greater acceleration. Since $F = ma$,then $a = F/m$. For the same force $F$,the vehicle with the smaller mass (the car) experiences higher acceleration.
$(iv)$ The car suffers more damage because it experiences a much higher magnitude of deceleration (acceleration) during the impact,leading to greater structural stress.

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$A$ man weighing $60 \, kg$ runs along the rails with a velocity of $18 \, km \, h^{-1}$ and jumps into a car of mass $1 \, \text{quintal} \, (100 \, kg)$ standing on the rails. Calculate the velocity with which the car will start travelling along the rails.

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