Pre-U Pre-U 9795/2 2018 June — Question 7

Exam BoardPre-U
ModulePre-U 9795/2 (Pre-U Further Mathematics Paper 2)
Year2018
SessionJune
TopicWork done and energy
TypeResistance as kv² - finding constant k
DifficultyModerate -0.3 This is a straightforward two-part mechanics question requiring standard energy/power formulas. Part (i) uses work-energy theorem with KE change plus PE change. Part (ii) applies P=Fv at constant speed where driving force equals resistance. Both parts are direct applications of standard A-level mechanics principles with no problem-solving insight required, making it slightly easier than average.
Spec6.02a Work done: concept and definition6.02b Calculate work: constant force, resolved component6.02l Power and velocity: P = Fv

7 A car has mass 800 kg .
  1. The car accelerates from \(10 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) to \(20 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) in climbing a hill with a vertical height of 16 m . Ignoring resistive forces, find the work done by the engine.
  2. The engine produces a constant power output of 189 kW . The car now travels along horizontal ground. Modelling the resistive force as \(7 v ^ { 2 } \mathrm {~N}\), where \(v \mathrm {~m} \mathrm {~s} ^ { - 1 }\) is the speed, find the value of \(v\) for which the speed of the car is constant.

7 A car has mass 800 kg .\\
(i) The car accelerates from $10 \mathrm {~m} \mathrm {~s} ^ { - 1 }$ to $20 \mathrm {~m} \mathrm {~s} ^ { - 1 }$ in climbing a hill with a vertical height of 16 m . Ignoring resistive forces, find the work done by the engine.\\
(ii) The engine produces a constant power output of 189 kW . The car now travels along horizontal ground. Modelling the resistive force as $7 v ^ { 2 } \mathrm {~N}$, where $v \mathrm {~m} \mathrm {~s} ^ { - 1 }$ is the speed, find the value of $v$ for which the speed of the car is constant.

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