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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.
After how much time, speed of particle decreases by `75%`

A

`(2l n2)/(alpha)`

B

`(l n(4//3))/(alpha)`

C

`(3V_(0))/(4alpha)`

D

`(e^(4))/(alpha)`

Text Solution

Verified by Experts

The correct Answer is:
D
After how ………….
`V = (V_(0))/(4) implies V_(0)e^(-alpha t)= (V_(0))/(4)`
`-alpha t = l n(1)/(4) implies t = (2l n2)/(alpha)`
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