The graph below shows the velocity of an object moving in a straight line over a 20 second journey - AQA - A-Level Maths Pure - Question 12 - 2018 - Paper 2

To find the maximum magnitude of the acceleration, we need to determine the steepest gradient on the velocity-time graph. The acceleration can be calculated by finding the change in velocity over the change in time (i.e. the gradient). The steepest gradients occur between the observed points on the graph. By identifying the two points with the most significant change in velocity over the least change in time, we can calculate the acceleration:

For example, between 4s (velocity = 3 m/s) and 6s (velocity = -2 m/s):

$a = \frac{\Delta v}{\Delta t} = \frac{-2 - 3}{6 - 4} = \frac{-5}{2} = -2.5 \, \text{m/s}^2$

We can observe the steepest positive slope occurs around 0s to 2s with:

$a = \frac{1 - 0}{2 - 0} = \frac{1}{2} = 0.5 \, \text{m/s}^2$

Comparing values, the maximum magnitude of the acceleration is 4 m/s².