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# Motion

## 08 Equation of Motion by Graphical Representation

#### EQUATION OF MOTION BY GRAPHICAL REPRESENTATION

The relation between quantities like velocity, time, acceleration and displacement provided the acceleration remains constant are collectively known as equation of motion.

#### FIRST EQUATION OF MOTION

The first equation of motion is:

Derivation of v= u + at by Graphical Method :

Initial velocity of the body  u = OA  ,  … (1)

And, Final velocity of the body  v = BC  … (2)

But from the graph    BC = BD + DC             and

Therefore,     v = BD + DC    … (3)

Again DC = OA

So, v = BD + OA

Now, from equation (1), OA = u

So,  v = BD + u

We should find out the value of BD now. We know that the slope of a velocity-time graph is equal to acceleration, a.

BD =  at

Now, putting this value of BD in equation (4) we get:

v = at + u

This equation can be rearranged to give:

v = u + at

#### SECOND EQUATION OF MOTION

Derivation of

by Graphical Method

……………………..(5)

……………………(6)

Distance travelled,

#### THIRD EQUATION OF MOTION

Distance travelled,   s = Area of trapezium OABC

Now, OA + CB = u + v  and OC = t. Putting these values in the above relation, we get:

v = u + at                         (first equation of motion)

And,  at = v – u

So,

or

or