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

Options

A. `(b^(2)tau)/(sqrt(2))`
B. `(b^(2)tau)/4`
C. `(b^(2)tau)/2`
D. `b^(2)tau`

Answer

C

Explanation

`u=bsqrt(x)`
`implies(dx)/(dt)=bsqrt(x)impliesint_(0)^(x)(dx)/(sqrt(x))=bint_(0)^(1)dt`
`implies2sqrt(x)=bt impliesx=(b^(2)t^(2))/4`
`impliesu=(dx)/(dt)=(b^(2)t)/2implies` velocity at `t=tau` is `v=(b^(2)tau)/2`