$A$ $8000 \,kg$ 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.

The following is the distance-time table of an object in motion:

Time in seconds	Distance in metres
$0$	$0$
$1$	$1$
$2$	$8$
$3$	$27$
$4$	$64$
$5$	$125$
$6$	$216$
$7$	$343$

$(a)$ What conclusion can you draw about the acceleration? Is it constant, increasing, decreasing, or zero?
$(b)$ What do you infer about the forces acting on the object?

Explain why some of the leaves may get detached from a tree if we vigorously shake its branch.

$A$ 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.

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.

$A$ 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.