A-LevelMathematicsMechanics9709/41 · Oct/Nov 2017 · Q58 Marks
A particle starts from a point O and moves in a straight line. The velocity of the particle at time t s after leaving O is v m s⁻¹, where v = 1.5 + 0.4t for 0 ≤ t ≤ 5, v = 100/t² - 0.1t for t ≥ 5.
- (i)Find the acceleration of the particle during the first 5 seconds of motion.[1]
- (ii)Find the value of t when the particle is instantaneously at rest.[2]
- (iii)Find the total distance travelled by the particle in the first 10 seconds of motion.[5]
Mark scheme
Marking points from the official mark scheme (Oct/Nov 2017). The mark or mark type is shown in brackets.
- [B1] Acceleration = 0.4 m s⁻²
- [M1] 100/t² - 0.1t = 0 For setting v = 0 and solving for t
- [A1] t = 10 s
- [B1] Distance t = 0 to t = 5 is ½ (1.5+3.5) × 5 = 12.5 Trapezium rule or integration
- [M1] s(t) = ∫(100/t² - 0.1t) dt For integration
- [A1] = -100/t – 0.05t² (+C) Correct integration
- [M1] s(10)-s(5) Use limits 5 and 10 used or find + C
- [A1] Total distance = 12.5 + 6.25 = 18.75 m
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