A-LevelMathematicsMechanics9709/41 · Oct/Nov 2022 · Q39 Marks

A constant resistance of magnitude 1400N acts on a car of mass 1250kg.

(a)The car is moving along a straight level road at a constant speed of 28 m s⁻¹. Find, in kW, the rate at which the engine of the car is working.[2]
(b)The car now travels at a constant speed up a hill inclined at an angle of θ to the horizontal, where sin θ = 0.12, with the engine working at 43.5 kW. Find this speed.[3]
(c)On another occasion, the car pulls a trailer of mass 600 kg up the same hill. The system of the car and the trailer is modelled as particles connected by a light inextensible cable. The car's engine produces a driving force of 5000N and the resistance to the motion of the trailer is 300N. The resistance to the motion of the car remains 1400 N. Find the acceleration of the system and the tension in the cable.[4]

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2022). The mark or mark type is shown in brackets.

[B1] Power = 1400×28
[B1] Power = 39.3kW
[B1] DF = 43500/v oe
[M1] Attempt to resolve parallel to the hill 3 terms, no need for DF in terms of v. Allow sign errors, sin/cos mix. Allow use of 6.89° or 6.9°.
[A1] Speed = 15 ms⁻¹ Awrt 15.0
[M1] Attempt at N2L on either car, trailer or the system Allow sign errors, sin/cos mix. Correct number of relevant terms. Allow use of 6.89° or 6.9°. Allow with g missing.
[A1] For any 2 equations correct.
[M1] Solve for a or T From equation(s) with at most 1 term. missing/extra in total. Allow with g missing.
[A1] Awrt 0.584 and 1370. a=0.583787838, T=1370.27027 .

On Oracle Prep you can write or photograph your own answer and have it marked by AI against this mark scheme, with feedback on what you missed.