| Exam Board | CAIE |
|---|---|
| Module | M1 (Mechanics 1) |
| Year | 2008 |
| Session | November |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Variable Force |
| Type | Constant power on horizontal road |
| Difficulty | Standard +0.3 This is a standard constant power mechanics problem requiring P=Fv to find driving force, then F=ma for deceleration, followed by finding equilibrium speed. Part (ii) involves showing the equilibrium speed is 20 m/s, which is straightforward algebra. Slightly above average difficulty due to the two-part structure and need to understand power-velocity relationship, but uses routine M1 techniques without requiring novel insight. |
| Spec | 3.02d Constant acceleration: SUVAT formulae6.02l Power and velocity: P = Fv6.02m Variable force power: using scalar product |
| Answer | Marks | Guidance |
|---|---|---|
| M1 | For applying Newton's second law (3 terms) | |
| \(F - 900 = 1200a\) | A1 | |
| \([18000/25 - 900 = 1200a]\) | M1 | For using \(F = P/v\) |
| Deceleration is \(0.15\text{ ms}^{-2}\) | A1 | [4] Accept \(a = -0.15\) |
| Answer | Marks | Guidance |
|---|---|---|
| \(18000/v - 900 = 0\) | B1 | |
| Least speed is \(20\text{ ms}^{-1}\) | B1 | [2] AG |
# Question 3:
## Part (i)
| M1 | For applying Newton's second law (3 terms)
$F - 900 = 1200a$ | A1 |
$[18000/25 - 900 = 1200a]$ | M1 | For using $F = P/v$
Deceleration is $0.15\text{ ms}^{-2}$ | A1 | [4] Accept $a = -0.15$
## Part (ii)
$18000/v - 900 = 0$ | B1 |
Least speed is $20\text{ ms}^{-1}$ | B1 | [2] AG
---3 A car of mass 1200 kg is travelling on a horizontal straight road and passes through a point $A$ with speed $25 \mathrm {~m} \mathrm {~s} ^ { - 1 }$. The power of the car's engine is 18 kW and the resistance to the car's motion is 900 N .\\
(i) Find the deceleration of the car at $A$.\\
(ii) Show that the speed of the car does not fall below $20 \mathrm {~m} \mathrm {~s} ^ { - 1 }$ while the car continues to move with the engine exerting a constant power of 18 kW .
\hfill \mbox{\textit{CAIE M1 2008 Q3 [6]}}