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

A particle moves with an initial velocity `v_(0)` and retardation `alp

1.	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 timeD. The velocity of particle will become `(v_(0))/(e)` after time `(1)/(alpha)`
Answer» Correct Answer - 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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