Name the physical quantity which corresponds to the rate of change of momentum.

What does the odometer of an automobile measure? Which of the following is moving faster? Justify your answer.
$(i)$ $A$ scooter moving with a speed of $300 \, m$ per minute.
$(ii)$ $A$ car moving with a speed of $36 \, km$ per hour.

Out of the three speed-time graphs shown below,identify the graph for the following cases:
$(i)$ $A$ ball thrown vertically upwards and returning to the hand of the thrower.
(ii) $A$ body decelerating to a constant speed and then accelerating.

Derive the following equations for a uniformly accelerated motion:
$(i)$ $v = u + at$
$(ii)$ $S = ut + \frac{1}{2}at^2$
$(iii)$ $v^2 - u^2 = 2aS$, where the symbols have their usual meanings.

What is the nature of the displacement-time graph of a body moving with constant velocity?

The following figure is the speed-time graph for a rocket from the moment when the fuel starts to burn,i.e.,at time $t=0$.
$(a)$ State the acceleration of the rocket at $t=0$.
$(b)$ State what happens to the acceleration of the rocket between $t=5 \, s$ and $t=60 \, s$.
$(c)$ Calculate the acceleration of the rocket at $t=80 \, s$. Give a reason for your answer.
$(d)$ The total mass of the rocket at $t=80 \, s$ is $1.6 \times 10^{6} \, kg$. Calculate the resultant force on the rocket at this time. Give a reason for your answer.