Question

Position verses time graph for a particle is shown in figure, then the correct alternative(s) for this are

• A. particle does not change its direction of motion during the motion from $t=0$ to $t=T$.
• B. particle changes its direction twice during the motion from $t=0$ to $t=T$.
• C. acceleration of particle changes its direction once during the motion from $t=0$ to $t=T$.
• D. direction of force is reversed at $t=\frac{T}{2}$.

Answer 1

Answer: (B), (D)

The correct options are
B particle changes its direction twice during the motion from $t=0$ to $t=T$.
D direction of force is reversed at $t=\frac{T}{2}$.

It can be interpreted with the help of slope as
$x=x_0+A\sin \omega t\frac{dx}{dt}=A\omega \cos \omega t\frac{d^{2}x}{d{t}^2}=-A{\omega }^2\sin \omega t$
Since at mean position the acceleration changes its direction where $t=\frac{T}{2}$. Hence force also changes direction at $t=\frac{T}{2}$