A-LevelMathematicsMechanics9709/42 · May/June 2019 · Q47 Marks
A constant resistance to motion of magnitude 350 N acts on a car of mass 1250 kg. The engine of the car exerts a constant driving force of 1200 N. The car travels along a road inclined at an angle of θ to the horizontal, where sin θ = 0.05. Find the speed of the car when it has moved 100 m from rest in each of the following cases. • The car is moving up the hill. • The car is moving down the hill.
- A constant resistance to motion of magnitude 350 N acts on a car of mass 1250 kg. The engine of the car exerts a constant driving force of 1200 N. The car travels along a road inclined at an angle of θ to the horizontal, where sin θ = 0.05. Find the speed of the car when it has moved 100 m from rest in each of the following cases. • The car is moving up the hill. • The car is moving down the hill.[7]
Mark scheme
Marking points from the official mark scheme (May/June 2019). The mark or mark type is shown in brackets.
- [M1] Apply Newton's second law for motion up the hill
- [A1] Correct Newton's law for motion up the hill
- [M1] Apply Newton's second law for motion down the hill
- [A1] Correct Newton's law for motion down the hill
- [M1] Use their a in the constant acceleration equations either to find v going up or going down the hill
- [A1] Up the hill: v = 6 ms⁻¹
- [A1] Down the hill: v = 15.4 ms⁻¹
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