Write true or false for the following statements

A motion is said to be uniform, if $x \propto t^{2}$

Give an example of a body which covers a certain distance, but its displacement is zero

A body thrown in the vertically upward direction rises upto a height $'h^{\prime}$ and comes back to the position of its start.

Calculate :

$(a)$ the total distance travelled by the body and

$(b)$ the displacement of the body. Under what condition will the magnitude of the displacement be equal to the distance travelled by an object ?

A car starts from rest and moves along the $x-$ axis with constant acceleration $5\, ms^{-2}$ for $8\,\sec $. If it then continues with constant velocity, what distance will the car cover in $12\,\sec $ since it started from the rest ?

Study the speed$-$time graph of a car below and answer the following questions

$(a)$ What type of motion is represented by $OA$ ?

$(b)$ Find acceleration from $B$ to $C$.

$(c)$ Calculate the distance covered by the body from $A$ to $B$.

Draw a diagram to show the motion of a body whose speed remains constant but velocity continuously changes.