In your everyday life,you come across a range of motions in which
$(a)$ acceleration is in the direction of motion.
$(b)$ acceleration is against the direction of motion.
$(c)$ acceleration is uniform.
$(d)$ acceleration is non$-$uniform.
Can you identify one example each of the above type of motion?

$(a)$ Derive the second equation of motion $S = ut + \frac{1}{2}at^2$ graphically,where the symbols have their usual meanings.
$(b)$ $A$ car accelerates uniformly from $18 \text{ km h}^{-1}$ to $36 \text{ km h}^{-1}$ in $5 \text{ s}$. Calculate the acceleration and the distance covered by the car in that time.

$(a)$ Draw velocity-time graphs for the following cases:
$(i)$ When the object is at rest.
$(ii)$ When the object is thrown vertically upwards.
$(b)$ $A$ motorcyclist riding motorcycle $A$ who is travelling at $36 \, km \, h^{-1}$ applies the brakes and stops the motorcycle in $10 \, s$. Another motorcyclist of motorcycle $B$ who is travelling at $18 \, km \, h^{-1}$ applies the brakes and stops the motorcycle in $20 \, s$. Plot the speed-time graph for the two motorcycles. Which of the two motorcycles travelled farther before it came to a stop?

$A$ girl running a race accelerates at $2.5 \, m s^{-2}$ for the first $4 \, s$ of the race. How far does she travel in this time (in $, m$)?

$A$ body is thrown vertically upward with velocity $u$,the greatest height $h$ to which it will rise is,

$A$ girl of mass $50\, kg$ jumps out of a moving boat of mass $300\, kg$ on to the bank with a horizontal velocity of $3\, m s^{-1}$. With what velocity does the boat begin to move backwards (in $, m s^{-1}$)?