PHYSICS · Multi-part · A Level · Physics · Mechanics and materials · Mechanics and materials
Problem
During the powered ascent of a small test rocket, onboard instrumentation records that the engine’s power output increases linearly with time, from P0=1.0×102W at launch (t=0) to Pf=7.0×102W at t=4.0s. Throughout this interval the rocket’s mass remains effectively constant, and all engine power is converted into the rocket’s mechanical energy.
(a) Derive an algebraic expression for the power P(t) as a function of time t during the 4-s burn.
(b) Determine the exact amount of work performed by the engine on the rocket during the burn, expressing your answer in joules.
(c) Calculate the rocket’s average power output over the 4-s interval and verify that it matches an appropriate geometric interpretation of the power–time graph.
(d) Discuss what the positive slope of P(t) implies about the engine’s operating conditions or fuel-combustion characteristics during the burn.