| Exam Board | CAIE |
|---|---|
| Module | M1 (Mechanics 1) |
| Year | 2017 |
| Session | June |
| Marks | 9 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Work done and energy |
| Type | Acceleration from power and speed |
| Difficulty | Moderate -0.3 This is a standard M1 power-force-velocity question requiring straightforward application of P=Fv and F=ma formulas. Part (i)(a) is direct substitution, (i)(b) involves finding new driving force then acceleration, and (ii) requires resolving forces on an incline. All steps are routine textbook exercises with no novel problem-solving required, making it slightly easier than average. |
| Spec | 6.02k Power: rate of doing work6.02l Power and velocity: P = Fv |
| Answer | Marks | Guidance |
|---|---|---|
| 4(ii) | DF = 80000/24 | B1 |
| [DF – 850 – mg sin θ = 0] | M1 | Newton 2 along the hill, 3 terms |
| Answer | Marks | Guidance |
|---|---|---|
| θ = ….. | M1 | Solve for θ, from a three term equation |
| θ = 11.9 | A1 | |
| Total: | 4 |
Question 4:
--- 4(ii) ---
4(ii) | DF = 80000/24 | B1 | DF = P/v
[DF – 850 – mg sin θ = 0] | M1 | Newton 2 along the hill, 3 terms
[12000 sin θ = 80000/24 – 850]
θ = ….. | M1 | Solve for θ, from a three term equation
θ = 11.9 | A1
Total: | 4A car of mass $1200$ kg is moving on a straight road against a constant force of $850$ N resisting the motion.
\begin{enumerate}[label=(\roman*)]
\item On a part of the road that is horizontal, the car moves with a constant speed of $42$ m s$^{-1}$.
\begin{enumerate}[label=(\alph*)]
\item Calculate, in kW, the power developed by the engine of the car.
[2]
\item Given that this power is suddenly increased by $6$ kW, find the instantaneous acceleration of the car.
[3]
\end{enumerate}
\item On a part of the road that is inclined at $\theta°$ to the horizontal, the car moves up the hill at a constant speed of $24$ m s$^{-1}$, with the engine working at $80$ kW. Find $\theta$.
[4]
\end{enumerate}
\hfill \mbox{\textit{CAIE M1 2017 Q4 [9]}}