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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.
total distance covered by the particle is

A

`(v_(0))/(2alpha)`

B

`(v_(0))/(alpha)`

C

`(3v_(0))/(2alpha)`

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
C
Total distance ……………
Retardation `=alpha V` ltbgt `V(dv)/(ds)= -alpha V implies overset(v)underset(v_(0))int dv= -alpha overset(s)underset(0)int ds`
`V-V_(0)= -alpha(S-0)`
`V = v_(0)-alpha S`
when particle stops `V = 0`
`V_(0)-alpha s = 0`
`S = (V_(0))/(alpha)`
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