Question

A car is moving with uniform velocity 'u' and acceleration 'a' covers a distance 's' in the time 't' . Draw its velocity - graph and derive the expression relating all the given physical quantities .

Answer 1

Here you go
Distance covered by the object = Area of rectangle + area of triangle

S = OA * OC + 1/2 * AD * BD
s = ut + 1/2 at * at
s = ut + 1/2 at^2

TAKE THE GRAPH FOR REFERENCE