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Question
How can you find the following?
Velocity from acceleration – time graph.
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Solution
Velocity from acceleration – time graph: Area under the acceleration – time graph gives the velocity of the body. When the body moves with variable velocity but uniform acceleration, then acceleration – time graph is a straight line (PQ) parallel to the time axis.
Take any two points A and B on PQ. From P and Q, draw perpendiculars (BC and AD) on the time axis. such that,
OD = t1 and OC = t2
Let OP = AD = BC = a = acceleration of the body.
Area under acceleration – time graph = area of rectangle ABCD
= AD × DC = AD × (OC − OD)
= a (t2 − t1)
= `("v"-"u")/(("t"_2-"t"_1))("t"_2-"t"_1)` = v − u
If initial velocity of the body = u = 0 Then area under acceleration – time graph = v – 0 = v = velocity of the body.
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