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)
Attachments:
Answers
Answered by
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.
Attachments:
Similar questions