Derive an expression for the velocity of the particle after covering distance s OR Derive the equation v2 = u2 + 2as using the velocity - time graph.
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particle moving along a straight line with a constant acceleration ‘a’. Let u be its velocity at time t = 0 and ‘v’ be the velocity after ‘t’ seconds. The velocity - time graph AC of this particle is shown in the figure.Distance travelled by the particle is given by,
s = area under v – t graph
= area of the trapezium OACD
= 1/2(OA + CD) × OD
But OA = u, CD = v and OD = t
∴ s = 1/2(u = v)t or
2s = (u + v)t ………(1)
But, a = slope of the graph = v – ut
∴ t = v – ua
On substituting in (1),
2s = (u + v)(v – ua)
i.e., v2 – u2 = 2as
or v2 = u2 + 2as