Question Detail

We have v² = k r. Also v = dr/dt. So (dr/dt)² = k r => dr/dt = √(k r). This is a differential equation. Solving: ∫ dr/√r = √k ∫ dt => 2√r = √k t + C. At t=0, r=0 => C=0. So 2√r = √k t => r = (k t²)/4. Then v = dr/dt = (k t)/2. At t=1 s, v = k/2. This is not in terms of r. So without knowing k, we cannot find a numerical value. The options given are in terms of k and r, but r at t=1 is k/4, so v = k/2 = 2r. Not among options. Option A is kr³/², B is kr, D is √(kr). None match. So data is insufficient to choose among these without knowing k or r. But since r at t=1 is k/4, then v = k/2 = 2r, which is not listed. So the answer is likely C: data is not sufficient.