$A$ bus starting from rest moves with a uniform acceleration of $0.1\, m s^{-2}$ for $2\, min$. Find $(a)$ the speed acquired,$(b)$ the distance travelled.

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?

$A$ 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?

$A$ stone is thrown in a vertically upward direction with a velocity of $5 \, m s^{-1}$. If the acceleration of the stone during its motion is $10 \, m s^{-2}$ in the downward direction,what will be the height attained by the stone and how much time will it take to reach there?

$A$ 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?

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.