A-LevelMathematicsMechanics9709/41 · Oct/Nov 2024 · Q78 Marks
A car has mass 1200kg. When the car is travelling at a speed of vms⁻¹, there is a resistive force of magnitude kv N. The maximum power of the car’s engine is 92.16kW.
- (a)(i)The car has a greatest possible constant speed of 48 ms⁻¹. Show that k = 40.[1]
- (a)(ii)At an instant when its speed is 45 ms⁻¹, find the greatest possible acceleration of the car.[3]
- (b)The car now travels at a constant speed up a hill inclined at an angle of sin⁻¹0.15 to the horizontal. Find the greatest possible speed of the car going up the hill.[4]
Mark scheme
Marking points from the official mark scheme (Oct/Nov 2024). The mark or mark type is shown in brackets.
- B1 Power = k×48² = 92160 ⇒ k = 40
- B1 [DF =] 92160/45 [= 2048]
- M1 2048-40×45=1200a
- A1 a = 248/1200 ms⁻²
- *M1 DF = 40v +1200g×0.15
- DM1 92160/v = 40v+1200g×0.15
- DM1 40v² + 1800v-92160 [=0]
- A1 v = 30.5 ms⁻¹
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