Challenging +1.2 This is a standard mechanics problem requiring application of P=Fv and Newton's second law in two scenarios. Students must set up two equations (one for uphill, one for downhill) involving the same unknowns P and a, then solve simultaneously. While it involves multiple steps and careful sign management for forces on slopes, it follows a well-established template for power-acceleration problems with no novel insight required.
6. A slope is inclined at an angle of \(5 ^ { \circ }\) to the horizontal. A car, of mass 1500 kg , has an engine that is working at a constant rate of \(P \mathrm {~W}\). The resistance to motion of the car is constant at 4500 N . When the car is moving up the slope, its acceleration is \(a \mathrm {~ms} ^ { - 2 }\) at the instant when its speed is \(10 \mathrm {~ms} ^ { - 1 }\). When the car is moving down the slope, its deceleration is \(a \mathrm {~ms} ^ { - 2 }\) at the instant when its speed is \(20 \mathrm {~ms} ^ { - 1 }\).
Determine the value of \(P\) and the value of \(a\).
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6. A slope is inclined at an angle of $5 ^ { \circ }$ to the horizontal. A car, of mass 1500 kg , has an engine that is working at a constant rate of $P \mathrm {~W}$. The resistance to motion of the car is constant at 4500 N . When the car is moving up the slope, its acceleration is $a \mathrm {~ms} ^ { - 2 }$ at the instant when its speed is $10 \mathrm {~ms} ^ { - 1 }$. When the car is moving down the slope, its deceleration is $a \mathrm {~ms} ^ { - 2 }$ at the instant when its speed is $20 \mathrm {~ms} ^ { - 1 }$.
Determine the value of $P$ and the value of $a$.\\
\includegraphics[max width=\textwidth, alt={}, center]{ae23a093-1419-4be4-8285-951650dc5a35-14_87_1609_635_267}\\
\hfill \mbox{\textit{WJEC Further Unit 3 2024 Q6 [10]}}