Challenging +1.2 This is a mechanics problem requiring systematic application of power-force relationships and resistance modeling. Students must set up two equations from the maximum speed conditions (power = driving force × velocity, with driving force balancing resistance and weight component), recognize that resistance R = kv², solve simultaneously for P and k, then calculate resistance at the given speed. While it involves multiple steps and careful algebraic manipulation, the approach is methodical and follows standard A-level mechanics techniques without requiring novel insight—moderately harder than average due to the algebraic complexity and Further Maths context.
A car of mass 750 kg is moving on a slope inclined at an angle \(\theta\) to the horizontal, where \(\sin\theta = 0.1\). When the car's engine is working at a constant power \(PW\), the car can travel at maximum speeds of \(14\text{ ms}^{-1}\) up the slope and \(28\text{ ms}^{-1}\) down the slope. In each case, the resistance to motion experienced by the car is proportional to the square of its speed. Find the value of \(P\) and determine the resistance to the motion of the car when its speed is \(10.5\text{ ms}^{-1}\). [10]
A car of mass 750 kg is moving on a slope inclined at an angle $\theta$ to the horizontal, where $\sin\theta = 0.1$. When the car's engine is working at a constant power $PW$, the car can travel at maximum speeds of $14\text{ ms}^{-1}$ up the slope and $28\text{ ms}^{-1}$ down the slope. In each case, the resistance to motion experienced by the car is proportional to the square of its speed. Find the value of $P$ and determine the resistance to the motion of the car when its speed is $10.5\text{ ms}^{-1}$. [10]
\hfill \mbox{\textit{WJEC Further Unit 3 2018 Q2 [10]}}