Question

The graph shows the velocity of a cyclist over time for this graph the area under the curve represents distance travelled.

use three strips of equal width to estimate the distance the cyclist travelled during this time.

Answer 1

Step-by-step explanation:

To make things simple, I first turned the graph 90 degrees. Then, I found two points and conducted a function for this parabola. At last, i use integration to find the area under the curve.

Answer 2

The cyclist traveled an estimated 52.5 meters.

To estimate the distance the cyclist travelled during this time using three strips of equal width, we can do the following:

Divide the graph into three equal strips.

Calculate the area of each strip by multiplying the average velocity of the cyclist over that interval by the width of the interval.

Add the areas of the three strips to estimate the total distance travelled.

Strip 1

Average velocity: (25 m/s + 20 m/s) / 2 = 22.5 m/s

Width: 1 s

Area: (22.5 m/s) * (1 s) = 22.5 m

Strip 2

Average velocity: (20 m/s + 15 m/s) / 2 = 17.5 m/s

Width: 1 s

Area: (17.5 m/s) * (1 s) = 17.5 m

Strip 3

Average velocity: (15 m/s + 10 m/s) / 2 = 12.5 m/s

Width: 1 s

Area: (12.5 m/s) * (1 s) = 12.5 m

Total distance travelled

Total distance travelled = Area of strip 1 + Area of strip 2 + Area of strip 3

= 22.5 m + 17.5 m + 12.5 m

= 52.5 m

Therefore, we can estimate that the cyclist travelled 52.5 meters during this time.