Question

Derive second equation of motion (s= ut + 1/2 at^2)

Answer 1

Let us 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. Here, The velocity-time graph is a straight

line AB

So, According to the velocity-time graph is

Att = 0, initial velocity= u = OA

At t = t, final velocity= v= OC

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

S= 1/2x (OA + DB) x OD

S= 1/2x (u + v) x t

Since v = u + at

S=1/2x (u+u+at) x t

s = ut + (1/2)at²

This is the required expression.