$A$ particle is moving in a circular path of radius $r$. The displacement after half a circle would be:

$(a)$ Differentiate acceleration from velocity.
$(b)$ Can a body have acceleration without change in magnitude of velocity? Explain with an example.
$(c)$ $A$ motor boat starting from rest on a lake accelerates in a straight line at a constant rate of $3 \, m s^{-2}$ for $8 \, s$. How far does the boat travel during this time?

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.

State whether the following statement is true or false:
$A$ motion is said to be uniform if a body undergoes equal displacements in equal intervals of time.

Identify what the graphs shown below indicate.

Derive the equation $v^{2}-u^{2}=2 a S$ graphically.