A constant power machine pulls a block on a smooth horizontal surface. Which one of the following correctly describes the relation between speed of the block (v) and time (t)?

  1. A. v \propto t
  2. B. v \propto \sqrt{t} ✓
  3. C. v \propto t^2
  4. D. v \propto t^{3/2}

Correct Answer: B. v \propto \sqrt{t}

Explanation

Power P = F \cdot v = m a v = m \left(\frac{dv}{dt}\right) v = \text{constant}. Separating variables and integrating gives v^2 = \left(\frac{2P}{m}\right)t, so v \propto \sqrt{t}.

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