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A particle is moving on a straight line and its distance `x` cms from a fixed point `O` on the line is given by`x=sqrt(t^(2)+1)` then the velocity of particle at `t=1` is

A

`1/(sqrt(2))`

B

`1/(sqrt(3))`

C

`1/(2sqrt(2))`

D

`1/(3sqrt(2))`

Text Solution

Verified by Experts

The correct Answer is:
A
Given `x=sqrt(t^(2)+1)`
Velocity `=V=(dx)/(dt)=(2t)/(2sqrt(t^(2)+1))`
`:.((dx)/(dt))_(t=1)=1/(sqrt(1+1))=1/(sqrt(2))`
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