A particle moves with an initial `v_(0)` and retardation alphav, where v is its velocity at any time t.
(i) The particle will cover a total distance `v_(0)/alpha`.
(ii) The particle will come to rest after time `1/alpha`.
(iii) The particle will continue to move for a very long time.
(iv) The velocity of the particle will become `v_(0)/2` after time `(1n2)/alpha`

Options

A. The particle will cover a total distance ` v_0//alpha `
B. The particle will come to rest after a time ` 1//alpha `
C. The particle will continue to move for a very long time
D. The velocity of the particle will become ` v_0//2 ` after a time ` 1//alpha `

Answer

A, C

Explanation

` a =-alpha v rArr int _(v_0) ^(v) (dv)/(v) =-alpha int _0^(t) dt rArr ln (v)/(v_0) =-alpha t rArr v=v_0 e^(-alpha t ) `
` int _0^(x) dx =v_0 int _0^(t) e ^(-alpha t ) rArr x= -(v_0)/(alpha ) (e^(-alpha t ) -1) " "therefore " "x= (v_0)/(alpha ) (l-e^(-alpha t)) `