O-LevelAdditional MathematicsDifferentiation and integration4037/22 · Oct/Nov 2012 · Q108 Marks
The acceleration, a ms⁻², of a particle, t s after passing through a fixed point O, is given by a = 4 – 2t, for t > 0. The particle, which moves in a straight line, passes through O with a velocity of 12 ms⁻¹.
- (i)Find the value of t when the particle comes to instantaneous rest.[5]
- (ii)Find the distance from O of the particle when it comes to instantaneous rest.[3]
Mark scheme
Marking points from the official mark scheme (Oct/Nov 2012). The mark or mark type is shown in brackets.
- [M1] Integrate to find v
- [A1] v = 4t – t²(+ c)
- [B1] Use t = 0, v = 12 to find c = 12
- [M1] v = 4t – t² + 12
- [A1] t = 6
- [M1] Integrate to find s
- [A1] s = 2t² – t³/3 + 12t
- [A1] s = 72
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