The distance$-$time graph of two trains are given below. The trains start simultaneously in the same direction.

$(i)$ How much ahead of $A$ is $B$ when the motion starts ?

$(ii)$ What is the speed of $B$ ?

$(iii)$ When and where $A$ will catch $B$ ?

$(iv)$ What is the difference between the speeds of $A$ and $B$ ?

$(v)$ Is the speed of either trains uniform or non uniform ? Justify your answer.

$(i)$ What can be depicted from the graph regarding the motion of the object ?

$(ii)$ Find the value of acceleration from the graph.

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 speed time graph for both the trains on the same paper. Also, calculate the distance travelled by each train after the brakes were applied.

$(a)$ Derive second equation of motion $S=u t+\frac{1}{2} a t^{2}$ graphically where the symbols have their usual meanings.

$(b)$ A car accelerates uniformly from $18\, km h ^{-1}$ to $36\, km h^{-1}$ in $5$ seconds. Calculate the acceleration and the distance covered by the car in that time.

$(a)$ Define uniform circular motion.

$(b)$ Is the uniform circular motion an accelerated motion? Give reasons for your answer.