Draw a velocity-time graph for a body moving with an initial velocity u and uniform acceleration a. Use this graph to find the distance travelled by the body in time t.

Below is the velocity-time graph for a body moving with an initial velocity u and uniform acceleration a:

Let v be the velocity at time t for this body having initial velocity u and uniform acceleration a as shown in the graph.

Distance travelled by the body in time t = Area under the velocity-time curve.

Hence,

Distance travelled = area of trapezium OABD

= $\dfrac{1}{2}$ x sum of parallel sides x height

= $\dfrac{1}{2}$ x (OA + DB) x OD

= $\dfrac{1}{2}$ x (u + v) x t

= $\dfrac{(\text{u} + \text{v})\text{t}}{2}$