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 time `(1)/(alpha)`
C. The particle will continue to move for a long time.
D. the velocity of particle will become `(v_(0))/(e)` after time `(1)/(alpha)`

Answer

A, C, D

Explanation

`v.(dv)/(dx)=-alphavimpliesorint_(v_(0))^(0)dv=-alphaint_(0)^(x_(0))dx`
`v_(0)=alphax_(0)impliesx_(0)=(v_(0))/(alpha)`,
`(dv)/(dt)=-alphav(or)int_(v_(0))^(v)(dv)/(v)=-alphaint_(0)^(t)dt`
`v=v_(0)e^(-alphat)(or)v=0for t=infty`
`impliesv=(v_(0))/(e)` when `t=(1)/(alpha)`