O-LevelAdditional MathematicsDifferentiation and integration4037/22 · May/June 2011 · Q78 Marks
A particle moves in a straight line so that, t s after passing through a fixed point O, its velocity, v ms⁻¹, is given by v = 60/(3t + 4)².
- (i)Find the velocity of the particle as it passes through O.[1]
- (ii)Find the acceleration of the particle when t = 2.[3]
- (iii)Find an expression for the displacement of the particle from O, t s after it has passed through O.[4]
Mark scheme
Marking points from the official mark scheme (May/June 2011). The mark or mark type is shown in brackets.
- [1] (i) 3.75 oe
- [1] (ii) a = dv/dt = k(3t + 4)⁻³
- [1] (ii) k = -360 oe
- [1] (ii) -0.36 oe
- [1] (iii) s = ∫ v dt = k(3t + 4)⁻¹ (+c)
- [1] (iii) k = -20 oe
- [1] (iii) Substitutes t = 0, s = 0 into k(3t + 4)ⁿ
- [1] (iii) 5 - 20/(3t+4) or 15t/(3t+4)
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