Standard +0.3 This is a standard M2 power-resistance problem requiring application of F=ma, resolving forces on an incline, and P=Fv. While it involves multiple steps (finding driving force from power, resolving parallel to slope, using Newton's second law), these are routine techniques that follow a well-practiced procedure with no novel insight required. The 9 marks reflect the working steps rather than conceptual difficulty, making it slightly easier than average.
6 A van, of mass 1400 kg , is accelerating at a constant rate of \(0.2 \mathrm {~m} \mathrm {~s} ^ { - 2 }\) as it travels up a slope inclined at an angle \(\theta\) to the horizontal.
The van experiences total resistance forces of 4000 N .
When the van is travelling at a speed of \(20 \mathrm {~m} \mathrm {~s} ^ { - 1 }\), the power output of the van's engine is 91.1 kW .
Find \(\theta\). [0pt]
[9 marks]
6 A van, of mass 1400 kg , is accelerating at a constant rate of $0.2 \mathrm {~m} \mathrm {~s} ^ { - 2 }$ as it travels up a slope inclined at an angle $\theta$ to the horizontal.
The van experiences total resistance forces of 4000 N .\\
When the van is travelling at a speed of $20 \mathrm {~m} \mathrm {~s} ^ { - 1 }$, the power output of the van's engine is 91.1 kW .
Find $\theta$.\\[0pt]
[9 marks]
\hfill \mbox{\textit{AQA M2 2015 Q6 [9]}}