A train starting from rest picks up a speed of $10\, m s ^{-1}$ in $100\, s$. It continues to move at the same speed for the next $250\, s$. It is then brought to rest in the nert $50\, s$. Plot a speed$-$time graph for the entire motion of the train.

$(i)$ acceleration of the train while accelerating,

$(ii)$ retardation of the train while retarding,

$(iii)$ and the total distance covered by the train.

A body is moving along a circular path of radius $R$. Find the displacement of the body when it completes half a revolution.

Two cars $A$ and $B$ have their displacement$-$time graph as given below. Which car has a greater velocity ?

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 body moves with a velocity of $2\, m s ^{-1}$ for $5\, s$, then its velocity increases uniformly to $10\, m s ^{-1}$ in next $5\, s.$ Thereafter, its velocity begins to decrease at a uniform rate until it comes to rest after $5\, s$.

$(i)$ Plot a velocity-time graph for the motion of the body.

$(ii)$ From the graph, find the total distance covered by the body after $2\, s$ and $12\, s$.