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Derive the 3 equations of motion using a graph.
(I)
u-initial velocity of objects. The body is moving with uniform acceleration 'a' let the object reaches at point 'B' after time 't' and its final velocity becomes 'v'.

Draw a line parallel to x-axis DA from point D where object starts moving.
Draw another line BA from point 'B' parallel to y-axis which meet at 'E' at y-axis.
Let OE = time 't' from graph BE=AB + AE
V = DC + OD (since AB = DC and AE = OD) v = DC + u  since OD =u
V = DC + u →(1)

by substituting value of DC from (2) in (1)
we get v = at + u
           v = u + at
This is the first equation of motion
(II)
Equation for distance time relation
Consider the trapezium ABDOE
Distance covered by the object in time 't' is given by the area of trapezium ABDOE.
Let m time 't' the distance covered by the moving object = s
Areas of trapezium = Area of △ABD + Area of ADOE

The above expression is known as second law of motion.
(III)
Third law of motion (Equation for distance velocity relation)
The distance covered by object moving with uniform acceleration is given by area of trapezium ABDOE
Area of trapezium
ABDOE = × Sum of parallel side + distance between parallel side
             = × (DO + BE) × OE
           s = (u + v) × t → (3)

After substituting the value of 't' from equation (4) in equation (3)

This is the third equation of motion


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