Challenging +1.2 This is a standard Further Maths mechanics problem requiring application of F=ma with power and resistance on an incline. It involves setting up two equations (one at acceleration, one at maximum velocity where a=0) and solving simultaneously. While it requires careful bookkeeping of forces and the P=Fv relationship, the method is routine for FM students with no novel insight needed. The 9 marks reflect multiple steps rather than exceptional difficulty.
A vehicle of mass 6000 kg is moving up a slope inclined at an angle \(\alpha\) to the horizontal, where \(\sin \alpha = \frac{6}{49}\). The vehicle's engine exerts a constant power of \(P\) W. The constant resistance to motion of the vehicle is \(R\) N. At the instant the vehicle is moving with velocity \(\frac{16}{5}\) ms\(^{-1}\), its acceleration is 2 ms\(^{-2}\). The maximum velocity of the vehicle is \(\frac{16}{3}\) ms\(^{-1}\).
Determine the value of \(P\) and the value of \(R\). [9]
A vehicle of mass 6000 kg is moving up a slope inclined at an angle $\alpha$ to the horizontal, where $\sin \alpha = \frac{6}{49}$. The vehicle's engine exerts a constant power of $P$ W. The constant resistance to motion of the vehicle is $R$ N. At the instant the vehicle is moving with velocity $\frac{16}{5}$ ms$^{-1}$, its acceleration is 2 ms$^{-2}$. The maximum velocity of the vehicle is $\frac{16}{3}$ ms$^{-1}$.
Determine the value of $P$ and the value of $R$. [9]
\hfill \mbox{\textit{WJEC Further Unit 3 Q7 [9]}}