| Exam Board | OCR |
|---|---|
| Module | Further Mechanics AS (Further Mechanics AS) |
| Year | 2020 |
| Session | November |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Power and driving force |
| Type | Find steady/maximum speed given power |
| Difficulty | Moderate -0.8 This is a straightforward application of the power-force-velocity relationship (P=Fv) and Newton's second law. Part (a) requires simple rearrangement of P=Fv at constant speed where driving force equals resistance. Part (b) uses F=ma after finding the driving force from power. Both parts are standard textbook exercises with direct formula application and minimal problem-solving required. |
| Spec | 6.02k Power: rate of doing work6.02l Power and velocity: P = Fv |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| At constant velocity, \(F = 250 = 10000/v\) | M1 | Tractive force \(= P/v =\) resistance |
| \(v = 40\) | A1 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| \(n = \frac{10000}{30}\) | M1 | Use of \(P = Dv\) where \(D\) is tractive force |
| \(\frac{10000}{30} - 250 = 1200a\) | M1 | Attempt NII with 2 forces (one of which could be just "\(D\)") |
| awrt \(0.069\) ms\(^{-2}\) | A1 |
## Question 1:
### Part (a)
| Answer | Marks | Guidance |
|--------|-------|----------|
| At constant velocity, $F = 250 = 10000/v$ | M1 | Tractive force $= P/v =$ resistance |
| $v = 40$ | A1 | |
### Part (b)
| Answer | Marks | Guidance |
|--------|-------|----------|
| $n = \frac{10000}{30}$ | M1 | Use of $P = Dv$ where $D$ is tractive force |
| $\frac{10000}{30} - 250 = 1200a$ | M1 | Attempt NII with 2 forces (one of which could be just "$D$") |
| awrt $0.069$ ms$^{-2}$ | A1 | |
---1 A car of mass 1200 kg is driven on a long straight horizontal road. There is a constant force of 250 N resisting the motion of the car. The engine of the car is working at a constant power of 10 kW .
\begin{enumerate}[label=(\alph*)]
\item The car can travel at constant speed $v \mathrm {~ms} ^ { - 1 }$ along the road. Find $v$.
\item Find the acceleration of the car at an instant when its speed is $30 \mathrm {~ms} ^ { - 1 }$.
\end{enumerate}
\hfill \mbox{\textit{OCR Further Mechanics AS 2020 Q1 [5]}}