$A$ $8000 \,kg$ engine pulls a train of $5$ wagons,each of $2000 \,kg$,along a horizontal track. If the engine exerts a force of $40000 \,N$ and the track offers a friction force of $5000 \,N$,then calculate the acceleration (in $m/s^2$) of the train.

$A$ hammer of mass $500 \,g$,moving at $50 \,m/s$,strikes a nail. The nail stops the hammer in a very short time of $0.01 \,s$. What is the force (in $N$) of the nail on the hammer?

Which of the following has more inertia: $(a)$ a rubber ball and a stone of the same size? $(b)$ a bicycle and a train? $(c)$ a five-rupee coin and a one-rupee coin?

$A$ bullet of mass $10\, g$ travelling horizontally with a velocity of $150\, m/s$ strikes a stationary wooden block and comes to rest in $0.03\, s$. Calculate the distance of penetration of the bullet into the block. Also,calculate the magnitude of the force exerted by the wooden block on the bullet.

$A$ hockey ball of mass $200 \,g$ travelling at $10 \,m \,s^{-1}$ is struck by a hockey stick so as to return it along its original path with a velocity of $5 \,m \,s^{-1}$. Calculate the magnitude of the change in momentum of the hockey ball due to the force applied by the hockey stick.

$A$ $8000 \,kg$ engine pulls a train of $5$ wagons,each of $2000 \,kg$,along a horizontal track. If the engine exerts a force of $40000 \,N$ and the track offers a friction force of $5000 \,N$,then calculate the net accelerating force (in $N$).