The graph below models the velocity of a small train as it moves on a straight track for 20 seconds - AQA - A-Level Maths Mechanics - Question 14 - 2017 - Paper 2

To find the total distance travelled, we need to calculate the area under the velocity-time graph, which can be divided into sections:

1. For the first part (0 to 6 seconds), the train moves at a constant velocity of 8 m/s:

   $S_1 = v imes t = 8 \text{ m/s} \times 6 \text{ s} = 48 \text{ m}$

2. For the second part (6 to 10 seconds), the train decelerates uniformly from 8 m/s to 0 m/s:

   $S_2 = \frac{1}{2} \times (v_1 + v_2) \times t = \frac{1}{2} \times (8 + 0) \times 4 = 16 \text{ m}$

3. For the third part (10 to 20 seconds), the train is stationary:

   $S_3 = 0 \text{ m}$

Now, summing these distances:

$S_{total} = S_1 + S_2 + S_3 = 48 + 16 + 0 = 64 \text{ m}$

Thus, the total distance travelled in 20 seconds is 64 meters.