Question

derive S=ut+1/2 at 2​

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. (Attachment)

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

Answer 2

Answer:

V=u+at -2 substitute 1 in 2

s=1/2t(u+u+at)

=1/2t(2u+at) s=ut+1/2at^2.