The graph shows the speed of a car, in metres per second, during the first 20 seconds of a journey - Edexcel - GCSE Maths - Question 16 - 2018 - Paper 3

To estimate the distance travelled, we can use the trapezoidal or rectangular area under the graph, divided into 4 strips of equal width.

1. Determine the width of each strip: The total time is 20 seconds, and we divide it into 4 strips, so each strip will have a width of: $ext{Width of each strip} = \frac{20 ext{ seconds}}{4} = 5 ext{ seconds}$

2. Calculate the area for each strip:

   • From 0 to 5 seconds, we read the height (speed) from the graph, which is approximately 10 m/s. The area is: $A_1 = 5 imes 10 = 50 ext{ metres}$
   • From 5 to 10 seconds, the speed is about 20 m/s: $A_2 = 5 imes 20 = 100 ext{ metres}$
   • From 10 to 15 seconds, the speed is about 30 m/s: $A_3 = 5 imes 30 = 150 ext{ metres}$
   • From 15 to 20 seconds, the speed is about 36 m/s: $A_4 = 5 imes 36 = 180 ext{ metres}$

3. Sum the areas to get the total distance: $ext{Total distance} = A_1 + A_2 + A_3 + A_4 = 50 + 100 + 150 + 180 = 480 ext{ metres}$

Thus, the estimated distance travelled by the car is approximately 480 metres.