If the displacement of a body is proportional to the time elapsed,what type of motion does the body possess?

$A$ cyclist driving at $5\, m s^{-1}$ picks up a velocity of $10\, m s^{-1}$ over a distance of $50\, m$. Calculate $(i)$ acceleration $(ii)$ time in which the cyclist picks up the above velocity.

Which of the following figures (Fig.) represents uniform motion of a moving object correctly?

Using the following data,draw a time-displacement graph for a moving object:

Time $(s)$	$0, 2, 4, 6, 8, 10, 12, 14, 16$
Displacement $(m)$	$0, 2, 4, 4, 4, 6, 4, 2, 0$

Use this graph to find the average velocity for the first $4 \, s$,for the next $4 \, s$,and for the last $6 \, s$.

$(a)$ Differentiate acceleration from velocity.
$(b)$ Can a body have acceleration without change in magnitude of velocity? Explain with an example.
$(c)$ $A$ motor boat starting from rest on a lake accelerates in a straight line at a constant rate of $3 \, m s^{-2}$ for $8 \, s$. How far does the boat travel during this time?

If the displacement of a body is proportional to the square of the time elapsed,what type of motion does the body possess?