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 22 - 2021 - Paper 3

To estimate the area under the graph using 3 trapeziums of equal width:

1. Determine the width of each trapezium: The total width from t = 1 to t = 4 is 3 seconds, so each trapezium will have a width of:

   $ext{Width} = \frac{3}{3} = 1 \text{ second}$

2. Find the corresponding speeds at each division:

   • At t = 1: Speed = 2 m/s
   • At t = 2: Speed = 4 m/s
   • At t = 3: Speed = 6 m/s
   • At t = 4: Speed = 8 m/s

3. Calculate the area of each trapezium:

   • Area of trapezium from t=1 to t=2:

     $A_1 = \frac{1}{2} \times (2 + 4) \times 1 = 3 ext{ m}$

   • Area of trapezium from t=2 to t=3:

     $A_2 = \frac{1}{2} \times (4 + 6) \times 1 = 5 ext{ m}$

   • Area of trapezium from t=3 to t=4:

     $A_3 = \frac{1}{2} \times (6 + 8) \times 1 = 7 ext{ m}$

4. Sum the areas:

   $ext{Total Area} = A_1 + A_2 + A_3 = 3 + 5 + 7 = 15 ext{ m}$

Therefore, the estimated area under the graph between t = 1 and t = 4 is 15 m.