The displacement of a body is proportional to the cube of the time lapsed. The magnitude of the acceleration is

A particle is moving in a circular path of radius $r$. The displacement after half a circle would be :

Name the force which is responsible for change in position or state of an object.

$(a)$ Draw velocity-time graph 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 themotorcycle in $20\, s$. Plot speed-time graph for the two motorcycles. Which of the two motorcycles travelled farther before it come to a stop ?

The velocity$-$time graph of an ascending passenger lift is as in the figure shown below

$(i)$ Identify the kind of motion of lift represented by lines $OA$ and $BC$.

$(ii)$ Calculate the acceleration of the lift

$(a)$ During the first two seconds.

$(b)$ Between the $3^ {r d}$ and $10^ {t h}$ second.

$(c)$ During the last two seconds.