A particle P moves in a straight line. The velocity v m s¯¹ at time t s is given by v = 4 + 0.2t for 0 ≤ t ≤ 10, v = -2 + 800/t² for 10 ≤ t ≤ 20.

Mark scheme

Marking points from the official mark scheme (Feb/Mar 2018). The mark or mark type is shown in brackets.

1. (i) [B1] 0.2 m s⁻²
2. (ii) [M1] Attempt differentiation of v = -2 + 800t⁻² (i.e., d/dt (800t⁻²))
3. (ii) [A1] a = -1600t⁻³ ; at t = 20, a = -1600 / 20³ = -0.2 m s⁻²
4. (iii) [B1] Straight line joining (0,4) and (10,6)
5. (iii) [B1] Curve with correct concavity (decreasing slope, becomes less negative) joining (10,6) to (20,0)
6. (iii) [B1] Correct labelling on axes, showing (0,4), (10,6), (20,0)
7. (iv) [B1] Distance for 0 ≤ t ≤ 10 is trapezium area: (4+6)/2 × 10 = 50 m
8. (iv) [M1] Attempt integration of v = -2 + 800t⁻² with respect to t
9. (iv) [A1] Correct indefinite integral: [-2t - 800t⁻¹]
10. (iv) [M1] Correct use of limits for 10 ≤ t ≤ 20: [-2(20) - 800/20] - [-2(10) - 800/10] = (-40 - 40) - (-20 - 80)
11. (iv) [A1] Total distance = 50 + 20 = 70 m