Challenging +1.2 This M4 question requires setting up the work-energy equation with variable resistance force (10v²), integrating to find work done against resistance, and applying the constant power relationship. While it involves calculus and careful algebraic manipulation across multiple steps (8 marks), it follows a standard M4 template for variable resistance problems without requiring novel insight—moderately above average difficulty due to the integration and algebraic complexity involved.
2. A car of mass 1000 kg , moving along a straight horizontal road, is driven by an engine which produces a constant power of 12 kW . The only resistance to the motion of the car is air resistance of magnitude \(10 v ^ { 2 } \mathrm {~N}\) where \(v \mathrm {~m} \mathrm {~s} ^ { - 1 }\) is the speed of the car.
Find the distance travelled by the car as its speed increases from \(5 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) to \(10 \mathrm {~m} \mathrm {~s} ^ { - 1 }\).
(8 marks)
2. A car of mass 1000 kg , moving along a straight horizontal road, is driven by an engine which produces a constant power of 12 kW . The only resistance to the motion of the car is air resistance of magnitude $10 v ^ { 2 } \mathrm {~N}$ where $v \mathrm {~m} \mathrm {~s} ^ { - 1 }$ is the speed of the car.
Find the distance travelled by the car as its speed increases from $5 \mathrm {~m} \mathrm {~s} ^ { - 1 }$ to $10 \mathrm {~m} \mathrm {~s} ^ { - 1 }$.\\
(8 marks)\\
\hfill \mbox{\textit{Edexcel M4 Q2 [8]}}