$A$ 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?

According to the third law of motion,when we push on an object,the object pushes back on us with an equal and opposite force. If the object is a massive truck parked along the roadside,it will probably not move. $A$ student justifies this by answering that the two opposite and equal forces cancel each other. Comment on this logic and explain why the truck does not move.

$A$ 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.

Two objects,each of mass $1.5\, kg$,are moving in the same straight line but in opposite directions. The velocity of each object is $2.5\, m/s$ before the collision during which they stick together. What will be the velocity (in $m/s$) of the combined object after collision?

$A$ motorcar of mass $1200\, kg$ is moving along a straight line with a uniform velocity of $90\, km/h$. Its velocity is slowed down to $18\, km/h$ in $4\, s$ by an unbalanced external force. Calculate the acceleration and change in momentum. Also,calculate the magnitude of the force required.

$A$ 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.