A particle starts from the origin at t = 0 and moves in the xy plane with constant acceleration a in the y-direction. Its equation of motion is y = bx². The x-component of its velocity is
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Question

A particle starts from the origin at t = 0 and moves in the xy plane with constant acceleration a in the y-direction. Its equation of motion is y = bx². The x-component of its velocity is

G1 Physics · Accepted Answer

Since acceleration is only along y, the x velocity is constant: x = vₓt. Also y = ½at². Eliminating t gives y = [a/(2vₓ²)]x². Comparing with y = bx² gives b = a/(2vₓ²), so vₓ = √[a/(2b)]. Hence option D.