Question

A particle starts with some initial velocity with an acceleration along the direction of motion. Draw a graph depicting the variation of velocity $\left(v\right)$ along y-axis with the variation of displacement $\left(s\right)$ along x-axis.

Answer 1

For uniformly accelerated motion, the relation between velocity $\left(v\right)$ and displacement (s) is given by $v^2=u^2=2as$.
Now, the above equation should be transformed to a suitable form, before the exact shape can be known.
$\therefore (v-0{)}^2=2a(s-\frac{u^2}{2a})$
which is of the form
$(y-k{)}^2=4a(x-h)$
The vertex is at $(h,k)$, i.e., $(\frac{u^2}{2a},0)$
and axis coincides with $x(i.e.,s)$ -axis.