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A particle is moving with speed v = b√x along positive x-axis. Calculate the speed of the particle at time t = τ (assume that the particle is at origin, t = 0)

1. b²τ/√2
2. b²τ
3. b²τ/2
4. b²τ/4

Correct answer: b²τ/2

Solution

v = b*sqrt(x) -> a = v(dv/dx) = b*sqrt(x) * b/(2*sqrt(x)) = b^2/2, a constant. Starting from rest at origin, v = a*t = (b^2/2)*tau = b^2*tau/2.

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