| Exam Board | CAIE |
|---|---|
| Module | M1 (Mechanics 1) |
| Year | 2018 |
| Session | June |
| Marks | 9 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Work done and energy |
| Type | Resistance as kv - finding constant k |
| Difficulty | Standard +0.3 This is a straightforward M1 mechanics question on power, force and motion. Part (i) uses P=Fv at terminal velocity where driving force equals resistance. Part (ii) applies F=ma with known maximum power. Part (iii) involves resolving forces on an incline with constant speed. All parts follow standard procedures with no novel problem-solving required, making it slightly easier than average. |
| Spec | 3.03c Newton's second law: F=ma one dimension6.02b Calculate work: constant force, resolved component6.02l Power and velocity: P = Fv |
| Answer | Marks |
|---|---|
| 6(i) | P |
| Answer | Marks | Guidance |
|---|---|---|
| 56 | M1 | Power |
| Answer | Marks |
|---|---|
| Power is 125 (kW) | A1 |
| Total: | 2 |
| Answer | Marks |
|---|---|
| 6(ii) | 125440 |
| Answer | Marks | Guidance |
|---|---|---|
| 32 | B1ft | Follow through their power from (i) |
| Answer | Marks | Guidance |
|---|---|---|
| 32 | M1 | For 3-term Newton II equation |
| a=1.89(ms−2) | A1 | |
| Total: | 3 | |
| Question | Answer | Marks |
| Answer | Marks |
|---|---|
| 6(iii) | 60000 |
| Answer | Marks | Guidance |
|---|---|---|
| 50 | M1 | For 3-term Newton II equation |
| A1 | Correct equation |
| Answer | Marks | Guidance |
|---|---|---|
| 14000 | M1 | |
| θ=3.3 | A1 | |
| Total: | 4 | |
| Question | Answer | Marks |
Question 6:
--- 6(i) ---
6(i) | P
[ =40×56]
56 | M1 | Power
For equating to Resistance, or equivalent
Velocity
Power is 125 (kW) | A1
Total: | 2
--- 6(ii) ---
6(ii) | 125440
Driving force is
32 | B1ft | Follow through their power from (i)
125440
[ −40×32=1400a]
32 | M1 | For 3-term Newton II equation
a=1.89(ms−2) | A1
Total: | 3
Question | Answer | Marks | Guidance
--- 6(iii) ---
6(iii) | 60000
[ +1400gsinθ−40×50=0]
50 | M1 | For 3-term Newton II equation
A1 | Correct equation
800
[sinθ°= ]
14000 | M1
θ=3.3 | A1
Total: | 4
Question | Answer | Marks | GuidanceA car of mass $1400\text{ kg}$ travelling at a speed of $v\text{ m s}^{-1}$ experiences a resistive force of magnitude $40v\text{ N}$. The greatest possible constant speed of the car along a straight level road is $56\text{ m s}^{-1}$.
\begin{enumerate}[label=(\roman*)]
\item Find, in kW, the greatest possible power of the car's engine. [2]
\item Find the greatest possible acceleration of the car at an instant when its speed on a straight level road is $32\text{ m s}^{-1}$. [3]
\item The car travels down a hill inclined at an angle of $\theta°$ to the horizontal at a constant speed of $50\text{ m s}^{-1}$. The power of the car's engine is $60\text{ kW}$. Find the value of $\theta$. [4]
\end{enumerate}
\hfill \mbox{\textit{CAIE M1 2018 Q6 [9]}}