Question

A PARTICLE CROSSING THE ORIGIN OF COORDINATES OF TIME T=0 MOVES IN XY PLANE WITH A CONSTANT ACCELERATION AA IN Y DIRECTION

Answer 1

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Answer 2

Given info : A particle starts from the origin of coordinates at time t=0 and moves in the xy plane with a constant acceleration α in the y-direction. Its equation of motion is y=βx²

To find : Its velocity component in the x-direction is..

Solution : here equation is y = βx²

difference with respect to time,

dy/dt = 2βx dx/dt

⇒vy = 2βx vx

a constant α is acting in y - direction.

So, vy = αt .....(1)

y = 1/2 αt²

from equation (1),

y = 1/2 α × vy²/α² = vy²/2α

So, y = βx² = vy²/2α

⇒x² = vy²/2αβ

⇒x = vy/√(2αβ) .......(2)

Now vy = 2βx vx

⇒vy = 2βvy/√(2αβ) vx

⇒√(2αβ)/2β = vx

⇒vx = √{α/2β}

Therefore the velocity component in the y - direction is √(α/2β)