Assertion: For a particle moving in a straight line velocity (v in m//s) of the particle in terms of time (t in sec) is given by `v = t^2 - 6t + 8`. Then the speed of the particle is minimum at `t = 2 sec`
Reason: For a particle moving in a straight line velocity `v` at any time `t` may be minimum or may be maximum when `(dv)/(dt) = 0`.

Options

A. If both assertion and reason are true and reason is the correct explanation of assertion.
B. If both assertion and reason are true but reason is not the correct explanation of assertion.
C. If assertion is true but reason is false.
D. If assersion is false but reason is true.

Answer

B

Explanation

The expression for velocity and time can be expressed as `v = (t - 2)(t - 4)`
The speed is therefore zero at `t = 2` and `t = 4`. Hence speed is minimum at `t = 2`.
But `(dv)/(dt) = 2t - 6` is zero at `t = 3` seconds.
Hence statement `I` is true also we know statement `II` is true but `II` is not a correct explanation of `I`.