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The power delivered by a force varies with time as: P increases linearly from 0 to P_max during time 0 to t0/2, then decreases linearly from P_max back to 0 during time t0/2 to t0 (a triangular power-time graph). The work done by the force for time t in the range 0 <= t <= t0 is:
- First increases then decreases
- First decreases then increases
- Always increases
- Always decreases
Correct answer: Always increases
Solution
Work done W(t) = integral₀^t P(t') dt'. If P(t) >= 0 for all t in [0,t0], then dW/dt = P(t) >= 0, meaning W is always increasing (or at worst constant). For a triangular P-t graph that starts at 0, rises to a peak, and returns to 0, P is always non-negative. Therefore W always increases throughout [0,t0]. The work increases faster in the first half (increasing P) and slower in the second half (decreasing P), but never decreases.
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