A particle starts from the origin of coordinates at time t = 0 and moves in the xy plane with a constant acceleration `alpha` in the y-direction. Its equation of motion is `y= betax^2`. Its velocity component in the x-direction is

Options

A. variable
B. `sqrt((2alpha)/(beta))`
C. `(alpha)/(2beta)`
D. `sqrt((alpha)/(2beta))`

Answer

D

Explanation

`y = betax^(2)`
`(dy)/(dt)=2betax((dx)/(dt))`
`(d^(2)y)/(dt^(2))=2beta[x((d^(2)x)/(dt^(2)))+((dx)/(dt))^(2)]`
`alpha=2betaV_(x)^(2)`
`V_(x)=sqrt((alpha)/(2beta))`