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 `:`

Options

A. aut
B. `1/a ln(aut)`
C. `1/a ln(1+aut)`
D. `aln(aut)`

Answer

C

Explanation

`alpha=-av^(2)=underset(u)overset(v)(int)(dv)/v^(2)=-a underset(t=0)overset(t)(int)dt`
`rArr -[1/v]_(u)^(v)=-atrArr 1/u-1/v=-at`
`rArr v=u/(1+aut)underset(0)overset(x)(int)dx=underset(t=0)overset(t)(int)(udt)/(1+aut)`
`rArr x=u/(au)[ln(1+aut)]_(0)^(t)=1/a ln(1+aut)`