$A$ motor bike running at $90 \, km \, h^{-1}$ is slowed down to $54 \, km \, h^{-1}$ by the application of brakes over a distance of $40 \, m$. If the brakes are applied with the same force,calculate $(i)$ the total time in which the bike comes to rest and $(ii)$ the total distance travelled by the bike.

State which of the following situations are possible and give an example of each of these:
$(a)$ $A$ body moving with constant acceleration but with zero velocity.
$(b)$ $A$ body moving horizontally with an acceleration in the vertical direction.
$(c)$ $A$ body moving with a constant speed in an accelerated motion.

$A$ stone is thrown vertically upward with an initial velocity of $40 \, m/s$. Taking $g = 10 \, m/s^2$,find the maximum height reached by the stone. What is the net displacement and the total distance covered by the stone?

Give examples to distinguish:
$(i)$ Distance and displacement.
$(ii)$ Speed and velocity.
$(iii)$ Acceleration and retardation.

For the motion on a straight line path with constant acceleration,the ratio of the magnitude of the displacement to the distance covered is

$(a)$ 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?