The displacement-time graph for a particle executing SHM is as shown in figure. Which of the following statements is correct?

Options

A. The velocity of the particle is maximum at `t=(3)/(4)T`.
B. The velocity of the particle is maximum at `t=(T)/(2)`
C. The acceleration of the particle is maximum at `t=(T)/(4)`
D. The acceleration of the particle is maximum at `t=(3)/(4)`T.

Answer

A

Explanation

For the given SHM,
The displacement of the particle is given by, `x=Acosomegat`
Velocity, `v=(dx)/(dt)=(d)/(dt)(Acosomegat)=-Aomegasinomegat`
Acceleration, `a=(dv)/(dt)=(d)/(dt)(-omegaAsinomegat)=-omega^(2)Acosomegat`
The corresponding velocity-time and acceleration time graph is as shown in the figure.