A particle moves in the positive x-direction according to v = αx + β/x, where α,β>0. At the point where its acceleration becomes zero, its position and speed are respectively:
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A particle moves in the positive x-direction according to v = αx + β/x, where α,β>0. At the point where its acceleration becomes zero, its position and speed are respectively:

G1 Physics · Accepted Answer

Since v is given as a function of x, a = v dv/dx. Here dv/dx = α − β/x². For a=0 and v≠0, α − β/x² = 0 ⇒ x = √(β/α). At this position, v = α√(β/α) + β/√(β/α) = √(αβ)+√(αβ) = 2√(αβ).