derive first equation of motion from velocity time graph of an object
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derive first equation of motion from velocity time graph of an object
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Derive the first equation of motion v = u + at, using the velocity- time graph for a body moving along a straight line with uniform acceleration.
Explanation:
Figures shows the change in velocity with time of a uniformly accelerated object. Object starts from the point in the graph with velocity u. Its velocity keeps increasing and after time t,it reaches the point B on the graph.
the initial velocity of the object = u = OD
The final velocity of the object = v = OC
Time = t = OE
Acceleration (a)= change in velocity
Time
=(Final velocity - Initial velocity
Time
=(OC - OD)
t
therefore, CD = at .......(1) (OC - OD = CD)
draw a line parallel to y axis passing through B. This will cross the x axis in E.
draw a line parallel to 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 1)
:. v = u + at
This is the first equation of motion