Define acceleration. State a relationship connecting $u, v, a$ and $t$ for an accelerated motion. Give an example of a motion in which acceleration is uniform.

Distinguish between the terms distance and displacement.

$(a)$ Derive the second equation of motion $S = ut + \frac{1}{2}at^2$ graphically,where the symbols have their usual meanings.
$(b)$ $A$ car accelerates uniformly from $18 \text{ km h}^{-1}$ to $36 \text{ km h}^{-1}$ in $5 \text{ s}$. Calculate the acceleration and the distance covered by the car in that 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.

$(a)$ Write differences between speed and velocity.
$(b)$ The speed of a moving object is $x \ m \ s^{-1}$. Its velocity is $y \ m \ s^{-1}$. What is the similarity observed?

The driver of a train $A$ travelling at a speed of $54\, km\, h^{-1}$ applies brakes and retards the train uniformly. The train stops in $5\, s$. Another train $B$ is travelling on the parallel track with a speed of $36\, km\, h^{-1}$. This driver also applies the brakes and the train retards uniformly. The train $B$ stops in $10\, s$. Plot the speed-time graph for both the trains on the same paper. Also,calculate the distance travelled by each train after the brakes were applied.