In previous Post we have drieve the Equation first of motion through graph

In this post we will drieve the Equation second of motion

Equation for Position time relation:

Let us consider that the object has travelled

a distance s in time t under uniform

acceleration a. the distance

travelled by the object is obtained by the area

enclosed within OABC under the velocity-time

graph AB.

Thus, the distance s travelled by the object

is given by

s = area Let us consider that the object has travelled
a distance s in time t under uniform
acceleration a. the distance
travelled by the object is obtained by the area enclosed inthe velocity time graph under OABC
graph AB.
Thus, the distance s travelled by the object
is given by
s = area OABC (which is a trapezium)
= area of the rectangle OADC + area of
the triangle ABD (which is a trapezium)

= area of the rectangle OADC + area of

the triangle ABD

= OA × OC +
1/2 (AD * BD)……. eq(1)
Substituting OA = u, OC = AD = t and

BD = at, in eq(1) we get

s = u*t + 1/2 a* t²

s = ut + 1/2 at²

These Equation of motion are very useful they will help us to know about the nature of motion of an object and also help us to know the other parameters if some are given we use these equations for solving numerical related kinematics.