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Draw the velocity-time graph for a particle moving with uniform acceleration a, starting with initial velocity vo, travelling for t seconds. De

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Class 11

>>Physics

>>Motion in a Straight Line

>>Speed and Velocity

>>Draw a velocity - time grap...

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Draw a velocity-time graph of uniformly accelerated motion in one dimension. From the velocity-time graph of uniformly accelerated motion deduce the equations of motion in distance and time.

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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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