Question

derive the second equation of motion i.e., s = ut + ¹/₂at²

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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