Here is a speed-time graph showing the speed, in metres per second, of an object t seconds after it started to move from rest - Edexcel - GCSE Maths - Question 23 - 2021 - Paper 3

Divide the Interval: The interval from t = 1 to t = 4 is 3 seconds long. Dividing this into 3 equal widths gives trapeziums of width 1 second each.

Identify Trapezium Heights: Find the speeds at each relevant time:

• At t = 1s, speed is approximately 2 m/s
• At t = 2s, speed is approximately 4 m/s
• At t = 3s, speed is approximately 6 m/s
• At t = 4s, speed is approximately 8 m/s

Calculate Area of Each Trapezium: Using the formula for the area of a trapezium, which is given by: $A = \frac{1}{2} \times (b_1 + b_2) \times h$ where ( b_1 ) and ( b_2 ) are the parallel sides (heights) and ( h ) is the width:

• Trapezium 1 (t = 1 to t = 2): $A_1 = \frac{1}{2} \times (2 + 4) \times 1 = 3$
• Trapezium 2 (t = 2 to t = 3): $A_2 = \frac{1}{2} \times (4 + 6) \times 1 = 5$
• Trapezium 3 (t = 3 to t = 4): $A_3 = \frac{1}{2} \times (6 + 8) \times 1 = 7$

Total Area: Sum the areas of the trapeziums: $ext{Total Area} = A_1 + A_2 + A_3 = 3 + 5 + 7 = 15$