A-LevelMathematicsMechanics9709/41 · Oct/Nov 2024 · Q87 Marks
A particle P moves in a straight line, passing through a point O with velocity 4.2 ms⁻¹. At time t s after P passes O, the acceleration, a ms⁻², of P is given by a = 0.6t-2.7. Find the distance P travels between the times at which it is at instantaneous rest.
- Find the distance P travels between the times at which it is at instantaneous rest.[7]
Mark scheme
Marking points from the official mark scheme (Oct/Nov 2024). The mark or mark type is shown in brackets.
- *M1 v = 0.3t² - 2.7t + c [c=4.2]
- DM1 0.3t² - 2.7t + 4.2 [= 0]
- A1 [(t-2)(t -7) = 0 ⇒] t = 2,7
- DM1 Attempt to integrate v
- A1 s = 0.1t³ - 1.35t² + 4.2t [+c]
- M1 For use of their positive t limits in their cubic expression for s
- A1 Total distance = 6.25 m
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