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?

How much momentum will a dumbbell of mass $10\, kg$ transfer to the floor if it falls from a height of $80\, cm$? Take its downward acceleration to be $10\, m \,s^{-2}$.

$A$ truck starts from rest and rolls down a hill with a constant acceleration. It travels a distance of $400 \, m$ in $20 \, s$. Find the force (in $N$) acting on it if its mass is $7 \, \text{tonnes}$ $(1 \, \text{tonne} = 1000 \, kg)$.

Akhtar, Kiran, and Rahul were riding in a motorcar that was moving with a high velocity on an expressway when an insect hit the windshield and got stuck on the windscreen. Kiran suggested that the insect suffered a greater change in momentum compared to the motorcar. Akhtar said that since the motorcar was moving with a larger velocity, it exerted a larger force on the insect. Rahul said that both the motorcar and the insect experienced the same force and the same change in momentum. Comment on these suggestions.

Two persons manage to push a motorcar of mass $1200 \, kg$ at a uniform velocity along a level road. The same motorcar can be pushed by three persons to produce an acceleration of $0.2 \, m \, s^{-2}$. With what force (in $N$) does each person push the motorcar? (Assume that all persons push the motorcar with the same muscular effort.)

$A$ 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?