When an object moves along a straight line with uniform acceleration, we can establish a relation between the velocity of the body, the acceleration of the body, and the displacement by the body in a particular time by a set of equations called Equations of Motion.

The three equations of motion are:-

1. V= u + at -- A velocity - time relation equation
2. S= ut + � at² -- A position - time relation equation
3. V2 � u2 = 2as -- A position - velocity relation equation

Equation for Velocity- Time Relation

Consider the velocity- Time Graph of an object that moves under uniform acceleration. Draw AD perpendicular to BC and BE perpendicular to OY. Let u be the initial velocity, it then increases to v (at point B), the final velocity in time t, and �a� is the acceleration of the body

According to the figure, V= BD + u
This implies v-u = BD

From the velocity time graph, acceleration of the object is :-
a= (change in velocity)/(time taken)
this implies a= BD/AD = BD/OC
this implies a= BD/t
or BD = a * t
Therefore from above we have, v-u = a * t
This implies v= u + at
Therefore the equation of velocity-time relation is v= u + at

Equations for Position - Speed Relationship

We know that the distance traveled by a uniformly accelerated body in time � t� is given by the area enclosed between the speed-time graph and the time axis.

Therefore, distance travelled s= area of trapezium OABC
S= (sum of parallel sides/ 2)* height
parallel sides are OA and CB and height is OC
S= (OA + CB)/2 * OC
Substituting the values of s = (u + v)/2 * t

We know v = u + at
So, t = (v-u)/a
Substituting the value of t in the equation:
S= (v + u)/2 *[(v-u)/a]
S=( v2 � u2) /2a
2as = v2 � u2
v2-u2 = 2as

Equations for Position � Time Relation

Let s be the distance traveled by the body in time t in going from A to B. We know that the distance traveled by an object is given by the area enclosed between the speed-time graph and the time axis i.e.

Distance, s = area of figure OABC
= area of rectangle OADC + area of triangle ABC
= OA * AC + � BD * AD
= u * t + � (BC � CD) * OC
= u*t + � (BC � OA) * OC
S= ut + � (v-u)t
S= ut + � (at) t

Read More: What is Acceleration? Uniform and Non-Uniform - Explanation