What is vet
v-t graph, Devive a
- using v-t graph
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A graph drawn by taking time along the x-axis and velocity along the y-axis is called a velocity-time graph. Consider a 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 in t seconds is given by,
s = area under v-t graph
= area of the triangle ABC + area of the rectangle ABDO
=1/2BC×AB+OA×OD From the graph,
BC = CD – BD = v – u,
AB = OD = t and OA = u
∴ s=1/2(v−u)t+ut …….. (1)
But, a = Slope of the graph = v−ut
∴ v – u = at
On substituting in (1) we have,
s=1/2at.t+ut
s=ut+1/2at^2
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