A-LevelMathematicsMechanics9709/42 · Oct/Nov 2020 · Q77 Marks
A particle P moves in a straight line, starting from a point O with velocity 1.72 m s⁻¹. The acceleration a m s⁻² of the particle, t s after leaving O, is given by a = 0.1t².
- (a)Find the value of t when the velocity of P is 3 m s⁻¹.[4]
- (b)Find the displacement of P from O when t = 2, giving your answer correct to 2 decimal places.[3]
Mark scheme
Marking points from the official mark scheme (Oct/Nov 2020). The mark or mark type is shown in brackets.
- [4] (a) ∫0.1t^(3/2)dt
- [4] (a) For integrating a
- [4] (a) v = 0.04t^(5/2)+1.72
- [4] (a) 0.04t^(5/2) +1.72=3
- [4] (a) For attempting to solve the equation v = 3, to obtain t
- [4] (a) t=4
- [3] (b) [∫(0.04t^(5/2) +1.72)dt]
- [3] (b) For integrating v which itself has come from integration
- [3] (b) [s=(2/175)t^(7/2) +1.72t(+C')]
- [3] (b) For using correct limits correctly
- [3] (b) Displacement when t = 2 is 3.57 m
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