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Equations of Motion by Graphical Method - Derivation of Velocity - Time Relation by Graphical Method

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Equation Describing the Relation Between Velocity and Time:

The velocity-time graph shows a uniformly accelerating object starting at point with initial velocity and reaching final velocity at point after time .

Initial velocity u = OD

Final velocity v = OC

Time t = OE

Acceleration (a) = `"Change in velocity"/"Time"` = `"(Final velocity – Initial velocity)"/"Time"` = `"(OC - OD)"/"t"`

CD = at   ...........(i)  (OC - OD = CD)

Draw a line parallel to the Y axis passing through B. This will cross the X axis in E. Draw a line parallel to the X-axis passing through D. This will cross the line BE at A.

From the graph... BE = AB + AE

v = CD + OD... (AB = CD and AE = OD)
v = at + u...........(from i )
v = u + at 

This is the first equation of motion.

Velocity-time graph

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