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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= betax^2`. Its velocity component in the x-direction is

A

variable

B

`sqrt((2alpha)/beta)`

C

`alpha/(2beta)`

D

`sqrt(alpha/(2beta))`

Text Solution

Verified by Experts

The correct Answer is:
D
`(dy)/(dt) = (2betax)*(dx)/(dt) and (d^2y)/(dx^2) = 2beta [(d^2x)/(dt^2) + ((dx)/(dt))^2]`
`(d^2y)/(dt^2) = alpha = a_y`
`(d^2 x)/(dt^2) = a_x = 0 and (dx)/(dt) = v_x`
`:. A`lpha = 2beta * v_(x)^2`
or `v_x = (sqrt(alpha/(2beta)))` .
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