The relation between quantities like velocity, time, acceleration and displacement provided the acceleration remains constant are collectively known as 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
by Graphical Method
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
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