Question

A particle starts with uniform acceleration. Draw a graph taking displacement $\left(s\right)$ of the particle along y-axis and time $\left(t\right)$ along x-axis. What is the curve known as?

Answer 1

While drawing the graph between any two quantities, the first step will be to establish a relation between them, in terms of known constants. Thus, for a uniformly accelerated motion, the relations between (s) and $\left(t\right)$ is $s=ut+\frac{1}{2}a{t}^2$.
But since $u=0$.
$\therefore s=\frac{1}{2}a{t}^2$
$s$ is taken along y-axis; replace $s$ by $y$ and, $t$ being along x-axis, replace $t$ by $x$.
Therefore, $y=\frac{a{x}^2}{2}$ or $x^2=\frac{2y}{a}$ which is of the form $x^2=4ay$.
Therefore, the graph will be parabola with its axis as $y$ i.e., $\left(s\right)$ axis.
Notice that the portion of graph to the left of the displacement axis (i.e., towards negative time) is omitted, as out point of interest lies in only the time elapsed after the beginning of motion.