Physics, asked by aayushi200314, 10 months ago

a particle starts from rest and its acceleration (a)plotted versus time (t) is shown in the given figure.Plot the corresponding: (a) Velocity (V) versus time (t) (b) displacement (S) versus time(t)​

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Answered by RitaNarine
5

Velocity versus time will be a straight line and displacement versus time will be a parabola.

From the given graph we can observe that acceleration a , is a constant with respect to time.

Therefore , a = K , a constant.

We know acceleration = rate of change of velocity.

  • a = dV/dt = K
  • dV = Kdt
  • Integrating  with respect to time,
  • V = Kt + Vo
  • Given particle starts from rest.
  • At t = 0, V = 0 ==> Vo  = 0

Therefore, equation of velocity is ,

  • V = Kt , is a straight line passing through origin.

Lets assume the object is at origin in the beginning.

We know velocity is the rate of change of position.

  • V = dx/dt
  • dx/dt = Kt
  • dx = Ktdt
  • Integrating with respect to time,
  • x = Kt²/2 + c
  • Since it is at origin at t= 0,
  • x = kt²/2
  • It is a parabola.

The plots can be observed from the attachment.

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