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A point moves in a straight line under t...

A point moves in a straight line under the retardation `av^(2)`, where `'a'` is a positive constant and `v` is speed. If the initial speed is `u`, the distance covered in `'t'` seconds is `:`

A

`a u t`

B

`(1)/(a)ln(a ut)`

C

`(1)/(a)ln(1+aut)`

D

`a ln (aut)`

Text Solution

Verified by Experts

The correct Answer is:
C
The retardation is given by `(dv)/(dt)=-av^(2)`
integrating between proper limits
`rArr-underset(u)overset(v)int(dv)/(v^(2))=underset(0)overset(t)inta dt`
or `(1)/(v)at+(1)/(u)`
`rArr(dt)/(dx)=at+(1)/(u)`
`rArrdx=(udt)/(1+aut)`
integrating between proper limits
`rArrunderset(0)overset(s)int dx=underset(0)overset(t)int (udt)/(1+aut)`
`rArr S=(1)/(a)ln(1+aut)`
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