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

Explanation

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 relation between (s) and (t) is `s=ut+(1)/(2)at^(2)`.
But since u=0,
`:. " " s=(1)/(2)at^(2)`
s is taken along y-axis, replace s by y and t being along x-axis , replace t by x.

Therefore, `y=(ax^(2))/(2)` or `x^(2)=(2y)/(a)` which is of the form ` x^(2)=4ay`.
Therefore, the graph will be parabola with its axis as y i. e., (s) axis.
Notice that the portion of graph to the left of the displacement axis (i.e., towards negative time ) is omitted, as our point of interest lies in only the time elapsed after the beginning of motion.