Question

A particle moves with an initial velocity v₀and retardation αv, where v is its velocity at any time t.

• A. The particle will cover a total distance v₀ /α.
• B. The particle will come to rest after a time 1/α.
• C. The particle will continue to move for a very long time.
• D. The velocity of the particle will become v₀/2 after a time 1 la.

Answer 1

Answer: (D)

The velocity of the particle will become v₀/2 after a time 1 la.

Answer 2

v$\frac { d v } { d x } = - \alpha v$

or $\int _ { v _ { 0 } } ^ { 0 } \mathrm { dx } = - \alpha \int _ { 0 } ^ { \mathrm { x } _ { 0 } } \mathrm { dx }$

or x_-0 =

or

or v = v₀e^-αt

∴ v = 0 for t → ∞.