$A$ 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 $4\, s$.

$A$ stone is dropped from the top of a tower. Its speed after it has fallen $20 \, m$ is (Take $g = 10 \, m s^{-2}$): (in $, m s^{-1}$)

$A$ cyclist driving at $36 \, km \, h^{-1}$ stops his cycle in $2 \, s$ by the application of brakes. Calculate $(i)$ retardation $(ii)$ distance covered during the application of brakes.

Obtain a relation for the distance travelled by an object moving with a uniform acceleration in the interval between the $4^{th}$ and $5^{th}$ seconds.

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?

$A$ 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?