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A particle moves with an initial velocity $υ_{0}$ and retardation $α υ,$ where $υ$ is velocity at any instant t. Then:

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The particle will cover a total distance $\frac{υ_{0}}{α}$

The particle continues to move for a long time span

The particle attains a velocity $\frac{1}{2} υ_{0}$ at $t = \frac{1}{α} .$

The particle comes to rest at $t = \frac{1}{α} .$

answer is A, B.

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Detailed Solution

$a = - α v$
$\frac{v d v}{d s} = - α v$
$\int_{v_{0}}^{0} d v = - α \int_{0}^{s} d s$
$0 - v_{0} = - α s$

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