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A car is moving with uniform velocity u and uniform acceleration a covers a distance s in time t draw its velocity time graph and derive an expression relating all given physical quantities.

Consider a particle moving along a straight line with uniform acceleration ‘a’its initial velocity is u and final velocity is v. Here we take velocity along X-axis  and time along Y-axis.

Area OPQS= Area of rectangle PRSO + Area of triangle PQR

                  =OP X OS + 1/2PR X QR

          OP=u,OS=t,PR=OS=t,QR=QS-RS=v-u

Area OPQS=u x t + ½ t (v-u)

But v-u=at

Area of OPQS=ut + ½ at²

S= ut + ½ at²