A particle is moving in a straight line with velocity $v \text{ ms}^{-1}$ at time $t$ seconds as shown by the graph below - AQA - A-Level Maths Mechanics - Question 15 - 2020 - Paper 2

To find an alternative estimate using the quadratic model, you can follow these steps:

1. Identify the quadratic equation: If a specific quadratic can closely fit the velocity values determined from the graph, determine its equation based on known points.

2. Integrate the quadratic: Use the quadratic function to compute the area under the curve over the interval $[20, 100]$ by evaluating the definite integral: $\int_{20}^{100} f(t) \, dt$ where $f(t)$ is the quadratic function.

3. Compare the results: This integration will provide a direct calculation of distance travelled, which can be compared to the distance calculated using the trapezium rule.