Question

A particle moves with an initial velocity v0 and retardation bv, where v is the velocity at any time t (b is a constant).
A) The particle will cover a total distance v0/b
B) The particle will continue to move for a very long time
C) The particle will stop shortly
D) The velocity of the particle will become (v0)/2 after time 1/b
Pick all options that apply.

Answer 1

" c "

Exaplanation :

Clearly particle is retarding, so after a time it will stop surely, when its velocity be 0.

Answer 2

Answer:

The particle will continue to move for a very long time

Explanation:

A particle moves with an initial velocity v0 and retardation bv, where v is the velocity at any time t (b is a constant).

a = dv/dt

a = -bv  ( - as retardation)

dv/dt  =  -bv

=> dv/v =  -bdt

integrating both sides

ln(v/v₀) = -bt

=> v/v₀ = e^(-bt)

=> v = V₀ e^(-bt)

so particle will never come to rest

=>  The particle will continue to move for a very long time

after t = 1/b

v = V₀e⁻¹ =  V₀/e   (at time = 1/b)