Question

The graph (in red) shows the speed (m/s) of a car for 36 seconds.

A triangle has been drawn underneath part of the curve to estimate the distance travelled
between 30 and 36 seconds.
By using an appropriate single trapezium under the first part of the graph, estimate the total
distance travelled by the car in those 36 seconds.
30 T Speed (m/s)
25
20
15
10
5
O
0 5
10
15
20
25
Tirhe (seconds)
30
35
40

Answer 1

To estimate the total distance traveled by the car in 36 seconds using a trapezium, we need to find the area under the curve of the graph. The trapezium can be constructed by connecting the points on the graph at the starting and ending times.

Let's break down the process into two parts:

Estimating the distance between 30 and 36 seconds:

To estimate the distance between 30 and 36 seconds, we can draw a triangle underneath that section of the curve. The base of the triangle is 6 seconds (36 - 30), and the height is the speed at 36 seconds (which is approximately 10 m/s). The area of the triangle is (base * height) / 2, so the estimated distance is (6 * 10) / 2 = 30 meters.

Estimating the distance using a trapezium:

To estimate the distance traveled in the first part of the graph (from 0 to 30 seconds), we can use a trapezium. The bases of the trapezium are the speeds at 0 and 30 seconds, which are approximately 25 m/s and 10 m/s, respectively. The height of the trapezium is the duration, which is 30 seconds. The area of the trapezium is ((base1 + base2) * height) / 2, so the estimated distance is ((25 + 10) * 30) / 2 = 525 meters.

Therefore, the estimated total distance traveled by the car in 36 seconds, using the trapezium and triangle approximation, is 30 meters + 525 meters = 555 meters.