Question

A body Falls freely from certain height show graphically the relation between distance fallen and the square of time how will you determine the from this graph

Answer 1

The graph will be a straight line with 0 intercept and g/2 slope as given in the equation..
Hope it helps

Answer 2

Given that,

A body Falls freely from certain height.

Suppose, the graph between distance and square of time shows the straight line.

We need to prove that the slope between distance fallen and the square of time shows the straight line

Using equation of motion

$s=ut+\dfrac{1}{2}gt^2$

Where, u = initial velocity

g = acceleration due to gravity

t = time

Here, object falls freely then the initial velocity zero.

$s=\dfrac{1}{2}gt^2$

Here, $\dfrac{g}{2}$ = constant

So, $s\propto t^2$

The distance fallen is directly proportional to square of time taken to reach the ground

Hence, In graphically, the slope shows the straight line.