$A$ driver of a train travelling at $40 \, m s^{-1}$ applies the brakes as the train enters a station. The train slows down at a rate of $2 \, m s^{-2}$. The platform is $400 \, m$ long. Will the train stop in time?

$A$ scooter starts from rest and moves in a straight line with a constant acceleration,covering a distance of $64 \, m$ in $4 \, s$.
$(i)$ Calculate its acceleration and its final velocity.
$(ii)$ At what time had the scooter covered half the total distance?

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?

Two stones are thrown vertically upwards simultaneously with their initial velocities $u_{1}$ and $u_{2}$ respectively. Prove that the heights reached by them would be in the ratio of $u_{1}^{2}: u_{2}^{2}$ (Assume upward acceleration is $-g$ and downward acceleration is $+g$).

$A$ motorboat starting from rest on a lake accelerates in a straight line at a constant rate of $3.0 \, m s^{-2}$ for $8.0 \, s$. How far does the boat travel (in $m$) during this time?

$A$ ball thrown up vertically returns to the thrower after $6\, s$. Find
$(a)$ the velocity with which it was thrown up,
$(b)$ the maximum height it reaches,and
$(c)$ its position after $4\, s$.