A sphere starts from rest in a viscous liquid under Stokes drag. Its time constant is τ = m/(6πηr) and its terminal speed is vₜ. What time is required for its speed to become vₜ/2?
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Question

A sphere starts from rest in a viscous liquid under Stokes drag. Its time constant is τ = m/(6πηr) and its terminal speed is vₜ. What time is required for its speed to become vₜ/2?

G1 Physics · Accepted Answer

For motion under a constant effective driving force and Stokes drag, v(t) = vₜ[1−exp(−t/τ)]. Set v(t) = vₜ/2. Then, 1/2 = 1−exp(−t/τ). Hence, exp(−t/τ) = 1/2. Taking logarithms, t/τ = ln2. Therefore, t = τ ln2. Correct option: B.