Define 'average speed'. An object moves with a uniform speed of $10\, m s ^{-1}$ for $5 s$ and then with a uniform speed of $5\, m s ^{-1}$ for $10\, s$. Find its average speed.

Under what condition will the displacement and distance have the same magnitude ?

Draw a velocity versus time graph for a body which starts to move with velocity $'u^{\prime}$ under a constant acceleration $'a'$ for time $t$. Using this graph derive an expression for distance covered $'S'$ in time $'t^{\prime}$

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.

If the displacement of an object is proportional to square of time, then the object moves with