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A particle is moving with speed v=bsqrt...

A particle is moving with speed `v=bsqrt(x)` along positive x-axis. Calculate the speed of the particle at time `t=tau` (assume that the particle is at origin at t = 0).

A

` b^(2) tau`

B

` ( b^(12) tau)/( 4)`

C

` ( b^(2) tau)/( sqrt(2))`

D

` ( b^(2) tau)/(2)`

Text Solution

Verified by Experts

The correct Answer is:
D
`v = ( dx)/( dt) = b sqrt( x)` . . . (i)
`rArr int _(0)^(x) ( dx)/( sqrt(x)) = int_(0)^(tau) b dt`
`rArr 2 sqrt(x) = b tau` . . . (ii) From the eq. (i) and (ii)
`rArr v = b ""( b tau)/(2) = ( b^(2) tau)/( 2)`
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