A force applied by an engine of a train of mass 2.05 x 10^6 kg changes its velocity from 5m/s to 25m/s in 5 minutes. The power of the engine is:
Correct answer: D. 2.05 MW
- A. 6 MW
- B. 1.025 MW
- C. 5 MW
- D. 2.05 MW
Explanation
The power of the engine is determined by the work done over time. First, calculate the change in kinetic energy, which is given by:ΔKE = 0.5 × mass × (vfinal2 - vinitial2) = 0.5 × 2.05×106 kg × ((25 m/s)2 - (5 m/s)2).Calculate ΔKE and then divide by the time in seconds (5 minutes = 300 seconds) to find power:Power = ΔKE / time = 2.05 MW.Other options result from errors in either the kinetic energy calculation or the conversion of time from minutes to seconds.
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Work transfers energy when a force causes displacement, while kinetic energy, gravitational potential energy and power describe motion, position and the rate of energy transfer. The work-energy theorem links net work with change in kinetic energy, and efficiency accounts for energy losses rather than treating them as energy destruction.
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