Question:
A body of mass 2 kg is driven by an engine delivering a constant power of 1 J/s. The body starts from rest and moves in a straight line. After 9 seconds, the body has moved a distance (in m) _______.
A body of mass 2 kg is driven by an engine delivering a constant power of 1 J/s. The body starts from rest and moves in a straight line. After 9 seconds, the body has moved a distance (in m) _______.
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Constant power: P t = (1/2) m v^2, so v is proportional to sqrt(t); integrate v dt.
Updated On: Nov 5, 2026
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Correct Answer: 18
Solution and Explanation
Work-energy theorem with constant power: \(P t = \frac{1}{2} m v^2\).
\(1 \times t = \frac{1}{2}(2) v^2 \Rightarrow v = \sqrt{t}\).
Distance: \(s = \int_0^9 \sqrt{t}\, dt = \frac{2}{3} t^{3/2}\Big|_0^9 = \frac{2}{3}\times 27 = 18\ \mathrm{m}\).
Answer: 18
\(1 \times t = \frac{1}{2}(2) v^2 \Rightarrow v = \sqrt{t}\).
Distance: \(s = \int_0^9 \sqrt{t}\, dt = \frac{2}{3} t^{3/2}\Big|_0^9 = \frac{2}{3}\times 27 = 18\ \mathrm{m}\).
Answer: 18
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