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A particle moves with an initial velocit...

A particle moves with an initial velocity `v_(0)` and retardation `alpha v`, where v is the velocity at any time t.

A

The particle will cover a total distance `(v_(0))/(alpha)`

B

the particle will come to rest after time `(1)/(alpha)`

C

the particle will continue to move for a along time

D

The velocity of particle will become `(v_(0))/(e)` after time `(1)/(alpha)`

Text Solution

Verified by Experts

The correct Answer is:
A, C, D
`v.(dv)/(dx) = - alpha v rArr ("or") underset(v_(0))overset(0)int dv = - alpha underset(0)overset(x_(0))int dx`
`v_(0) = alpha x_(0) rArr x_(0) = (v_(0))/(alpha)`,
`(dv)/(dt) = - alpha v ("or") underset(v_(0))overset(v)int (dv)/(v) = - alpha underset(0)overset(t)int dt`
`v = v_(0)e^(-alpha t) ("or") v = 0` for `t = oo`
`rArr v = (v_(0))/(e)` when `t = (1)/(alpha)`
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