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The displacement of a body is given by r...

The displacement of a body is given by `r = sqrt(a^(2)-t^(2))+ t cos t^(2)`, where `t` is the time and a is constant. Its velocity is :

A

`(-t)/(sqrt(a^(2)-t^(2)))+cost^(2)-tsin2t`

B

`(-t)/(sqrt(a^(2)-t^(2)))+cost^(2)-2t^(2)sin2t^(2)`

C

`(-a)/(sqrt(a^(2)-t^(2)))+2tcost^(2)sint+sin2t`

D

`a-t^(2)-tsint^(2)`

Text Solution

Verified by Experts

The correct Answer is:
B
`r=sqrt(a^(2)-t^(2))+tcost^(2)`
`V=(dr)/(dt)=(1)/(2)(a^(2)-t^(2))^(-1//2)(-2t)+t(-sint^(2))2t+cost^(2)`
`V=-(1)/(sqrt(a^(2)-t^(2)))-2t^(2)sint^(2)+cost^(2)`.
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