A train is travelling at a speed of $90\, km h ^{-1}$. Breaks are applied so as to produce a uniform acceleration of $0.5\, m s ^{-2}$. Find how far the train will go before it is brought to rest.

An object is moving along a straight line with uniform acceleration. The following table gives the velocity of the object at various instants of time

Plot the graph.

From the graph.

$(i)$ Find the velocity of the object at the end of $2.5 sec$

$(ii)$ Calculate the acceleration.

$(iii)$ Calculate' the distance covered in the last $4$ sec.

Using following data, draw time-displacement graph for a moving object :

Use this graph to find average velocity for first $4\,\sec $, for next $4\,\sec $ and for last $6\,\sec $.

An electron moving with a velocity of $5 \times 10^{4}\, ms ^{-1}$ enters into a uniform electric field and acquires a uniform acceleration of $10^{4}\, ms ^{-2}$ in the direction of its initial motion.

$(i)$ Calculate the time in which the electron would acquire a velocity double of its initial velocity.

$(ii)$ How much distance the electron would cover in this time ?

The $v-t$ graph of cars $A$ and $B$ which start from the same place and move along straight road in the same direction, is shown. Calculate

$(i)$ the acceleration of car $A$ between $0$ and $8\, s$.

$(ii)$ the acceleration of car $B$ between $2\, s$ and $4\, s$.

$(iii)$ the points of time at which both the cars have the same velocity.

$(iv)$ which of the two cars is ahead after $8\, s$ and by how much ?