Question

Derive an equation for position - time (s= ut + 1/2at^2 ) relation for an object that travelled a distance 's' in time 't' under uniform acceleration 'a'.​

Answer 1

Consider the linear motion of a body with an initial velocity U.

Let the body accelerate uniformly and acquire a final velocity V after time T.

The velocity–time graph is a straight line AB as shown below.

At t = 0, initial velocity = u = OA

At t = t, final velocity = v = OC

The distance S travelled in time t = area of the trapezium OABD

s = (1/2) x (OA + DB) × OD

s = (1/2) x (u + v) × t

Since v = u + at,

s = (1/2) x (u + u + at) × t

s = ut + (1/2) at2

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