Moderate -0.3 This is a standard connected particles problem requiring application of F=ma to two bodies, use of P=Fv to find driving force, and solving simultaneous equations. The setup is straightforward with clearly stated resistances and a single speed given. While it requires multiple steps (finding driving force, applying Newton's second law to system and trailer separately), these are routine techniques for M1 students with no conceptual subtlety or novel insight required.
4 A car of mass 1700 kg is pulling a trailer of mass 300 kg along a straight horizontal road. The car and trailer are connected by a light inextensible cable which is parallel to the road. There are constant resistances to motion of 400 N on the car and 150 N on the trailer. The power of the car's engine is 14000 W .
Find the acceleration of the car and the tension in the cable when the speed is \(20 \mathrm {~ms} ^ { - 1 }\).
Attempt at Newton's second law on car or trailer or system
*M1
Correct number of relevant terms (e.g. correct masses); allow sign errors
\(700 - 400 - T = 1700a\)
A2
A1 for one correct and A2 for any two correct. May have \(DF\) (or *their* \(DF\)) for 700 but A0 if using 14000 as \(DF\) without first stating \(DF\). Must have same \(T\) if using first two equations for A2
\(T - 150 = 300a\)
\(700 - 400 - 150 = (1700 + 300)a\)
Solving for \(a\) or \(T\)
DM1
From equations with the correct number of relevant terms. For both correct answers
## Question 4:
| Answer | Mark | Guidance |
|--------|------|----------|
| Driving force $= \dfrac{14000}{20}$ $[= 700]$ | B1 | OE, e.g. $20 \times DF = 14000$ |
| Attempt at Newton's second law on car or trailer or system | *M1 | Correct number of relevant terms (e.g. correct masses); allow sign errors |
| $700 - 400 - T = 1700a$ | A2 | A1 for one correct and A2 for any two correct. May have $DF$ (or *their* $DF$) for 700 but A0 if using 14000 as $DF$ without first stating $DF$. Must have same $T$ if using first two equations for A2 |
| $T - 150 = 300a$ | | |
| $700 - 400 - 150 = (1700 + 300)a$ | | |
| Solving for $a$ or $T$ | DM1 | From equations with the correct number of relevant terms. For both correct answers |
| Acceleration $= \dfrac{3}{40} = 0.075\text{ ms}^{-2}$ | | |
| Tension $= 172.5\text{ N}$ | A1 | Condone 173 |
| | **6** | |
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4 A car of mass 1700 kg is pulling a trailer of mass 300 kg along a straight horizontal road. The car and trailer are connected by a light inextensible cable which is parallel to the road. There are constant resistances to motion of 400 N on the car and 150 N on the trailer. The power of the car's engine is 14000 W .
Find the acceleration of the car and the tension in the cable when the speed is $20 \mathrm {~ms} ^ { - 1 }$.\\
\hfill \mbox{\textit{CAIE M1 2024 Q4 [6]}}