Draw (i) position-time (ii) velocity-time and (iii) acceleration-time graph for the motion of an object under free fall.

Explanation

We assume the downward direction as the positive direction during this free fall.

(i) As u =0 , the displacement at any time t is h = `(1)/(2)"gt"^(2) " ""or"" " t^(2) = (2)/(g)h`.
So the position-time graph is a parabola passing through the origin [ like `x^(2) = 4 ay` on a x-y graph].
(ii) Initial velocity u = 0 so at any time t the velocity is v =gt.
Hence the velocity-time graph is a straight line of positive slope passing through the origin [ like y = mx on a xy -graph]
(iii) Acceleration (a) = acceleration due to gravity (g) = constant and positive.
So the acceleration-time graph is parallel with time axis.