Question

Assertion :A student performed an experiment by moving a certain block in a straight line. The velocity position graph is as shown in the figure. The particle has zero velocity after infinite time. Reason: When a particle is at its maximum position in rectilinear motion its velocity must be zero.

• A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.
• B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion.
• C. Assertion is correct but Reason is incorrect.
• D. Assertion is incorrect but Reason is correct.

Answer 1

The correct option is B Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion.

In the given plot,

$v=-kx+c$ where $k$ and $c$ are positive constants.

$\frac{dv}{dx}=-k$

Acceleration is given by:

$a=\frac{vdv}{dx}=-kv$

$\frac{dv}{dt}=-kv$

or $v\left(t\right)=v\left(0\right)e^{-kt}$

$v\left(t\right)=c{e}^{-kt}$

Clearly, the particle has zero velocity after infinite time.

When the particle is at its maximum position then at that instant the particle reverses its direction or come to rest. Thus the velocity of the particle is zero at that instant. However, this does not explain why the particle takes infinite time to stop.