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A particle starts from the origin of coo...

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 = beta x^(2)`. Its velocity component in the x-directon is

A

Variable

B

`sqrt((2alpha)/(beta))`

C

`(alpha)/(2beta)`

D

`sqrt((alpha)/(2beta))`

Text Solution

Verified by Experts

The correct Answer is:
D
`y=beta x^(2), (d^(2)y)/(dt^(2))=alpha, (d^(2)x)/(dt^(2)=0`
`(dy)/(dt) =2beta x (dx)/(dt) rArr (d^(2)y)/(dt^(2))=2betax (d^(2)x)/(dt^(2))+2beta ((dx)/(dt))^(2)`
`rArr 2beta((dx)/(dt))^(2) =alpha rArr (dx)/(dt)=v_(x)=sqrt((alpha)/(2beta))`
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