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A particle moves with an initial velocit...

A particle moves with an initial velocity `V_(0)` and retardation `alpha v` , where `alpha` is a constant and v is the velocity at any time t.
Velocity of particle at time is :

A

`v = alpha t^(2)`

B

`v = V_(0) - alpha t`

C

`v = (V_(0))/(ln alpha t)`

D

`v = V_(0)e^(-alpha t)`

Text Solution

Verified by Experts

The correct Answer is:
B
Velocity of …………..
`(dv)/(dt) = -alpha v`
`overset(v)underset(v_(0))int (dv)/(v) = -alpha overset(t)underset(0)int dt`
`|l nv|_(v_(0)^(v)= -alpha|t|_(0)^(t)`
In `(V)/(V_(0))= - alpha t`
`V = V = V_(0)e^(-alpha t)`
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