A flight computer calculates the total distance traveled by an autonomous drone by applying the trapezium rule to velocity data v(t)v(t)v(t) sampled over the interval 1≤t≤51 \le t \le 51≤t≤5. The computer evaluates four different mathematical models for the drone's velocity:
Model A: v(t)=3t+4v(t) = 3t + 4v(t)=3t+4
Model B: v(t)=12ln(t)v(t) = 12\ln(t)v(t)=12ln(t)
Model C: v(t)=12et/2v(t) = \frac{1}{2}e^{t/2}v(t)=21et/2
Model D: v(t)=10+4t−t2v(t) = 10 + 4t - t^2v(t)=10+4t−t2
Identify which model will result in the trapezium rule producing an overestimate of the actual distance traveled. Justify your answer.
125 exam-style questions on AQA A Level Maths 1.12 I: Numerical methods (A-level only), covering 1.12.1 Locating roots by change of sign (A-level only), 1.12.2 Iterative methods and Newton-Raphson (A-level only), 1.12.3 Numerical integration (A-level only), and 1.12.4 Numerical methods in context (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.