A sphere moving under Stokes drag has time constant 2 s. Starting from rest, the time required to reach half its terminal speed is N ln2 seconds. Find N.

Question

G1 Physics · Accepted Answer

For Stokes motion, v(t) = vₜ[1−exp(−t/τ)]. At half terminal speed, v = vₜ/2. Therefore, t = τ ln2. Given, τ = 2 s. Hence, t = 2 ln2 s. Therefore, N = 2.