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?

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.)

$(a)$ Define momentum and mention its $SI$ unit.
$(b)$ From the velocity-time graph shown in the figure for a body of mass $5\, kg$,find the force on the body from:
$(i)$ $O$ to $A$ and $(ii)$ $B$ to $C$.
$(c)$ Which would require a greater force: accelerating a $2\, kg$ mass at $5\, m s^{-2}$ or a $4\, kg$ mass at $2\, m s^{-2}$?

$A$ sledge of mass $80 \, kg$ moves over the frozen surface of a lake with a velocity of $30 \, m s^{-1}$ and comes to rest in $5 \, s$. Find its negative acceleration and the frictional force between the lake and the sledge.

$(i)$ Name the property of bodies to resist a change in their velocity.
$(ii)$ What is the relationship between force and acceleration?
$(iii)$ What name is given to the product of mass and velocity of a body?
$(iv)$ Which physical quantity corresponds to the rate of change of momentum?
$(v)$ Name the principle on which a rocket works.

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?