In previous Post we have drieve the Equation second of motion which establish the relation between position and time.
In this post we will drieve the Equation third of motion which will establish relation between position and velocity of object.
Equation for Position velocity relation :
From the velocity-time graph shown above the distance s travelled by the
Object in time t,moving under uniform acceleration
a, is given by the area enclosed within the
trapezium OABC under the graph i. e.
s = area of the trapezium OABC
=((OA + BC) *OC) /2
Substituting OA = u, BC = v and OC = t,
we get
s =(( v+u) *t) /2………eq(1)
From the velocity-time relation
v = u + at
we get
t= v-u /a………. eq(2)
Using Eqs. (1) and (2) we have
(v+u) (v-u ) /2a = s
or
2 a s = v² – u²
It is known as position velocity relation or Equation third of motion we can see that it is establishing relation between position of an object and velocity of an object.
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.