A-LevelMathematicsMechanics9709/41 · May/June 2022 · Q59 Marks

Two racing cars A and B are at rest alongside each other at a point O on a straight horizontal test track. The mass of A is 1200kg. The engine of A produces a constant driving force of 4500N. When A arrives at a point P its speed is 25ms¯¹. The distance OP is dm. The work done against the resistance force experienced by A between O and P is 75000J.

(a)Show that d = 100.[3]
(b)Car B starts off at the same instant as car A. The two cars arrive at P simultaneously and with the same speed. The engine of B produces a driving force of 3200N and the car experiences a constant resistance to motion of 1200 N. Find the mass of B.[3]
(c)Find the steady speed which B can maintain when its engine is working at the same rate as it is at P.[3]

Mark scheme

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

[M1] For attempt at work energy equation (3 terms. Allow sign errors. M0 for (constant) acceleration method)
[A1] 4500d - 75 000 = 1/2 * 1200 * 25² [= 375 000] (Correct equation)
[A1] d = 100 (AG, Accept verification with d substituted in above line to show LHS = 375000 or LHS-RHS = 0. If no marks scored allow SCB1 for 1/2*1200*25²)
[B1] 25² = 0 + 2a*100 [leading to a = 3.125] (Allow B1 if acceleration found in part (a) as 3.125 and used or stated here)
[M1] 3200 - 1200 = m * 3.125 (Newton's second law with 3 terms. Allow sign errors and their a.)
[A1] Mass of car B = 640 kg
[B1] At P power = 3200 * 25 [= 80 000] (For use of power = Fv)
[M1] Attempt Newton's second law for car B with a = 0 (80000/v - 1200 = 0) (Allow their 80 000 (dimensionally correct))
[A1] Steady speed = 66.7 ms⁻¹ (Allow 200/3 = 66 2/3)

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