t(s)=0.0,1.0,2.0,3.0,4.0,5.0,6.0,7.0

v(m/s)=0.0,4.6,8.9,13.4,18.0,22.9,27.6,32.0
find the area underneath the graph between t=2.0s and t=6.0s, i know i will have to break this down into two separate shapes, a rectangle and a triangle then add them together, i just don't know how to , then the other part id what is the distance traveled between t=2.0s and t=6.0s ?

To find the area underneath the graph between t = 2.0s and t = 6.0s, we can break it down into two separate shapes: a rectangle and a triangle.

1. Rectangle:
To find the area of the rectangle, you need to multiply the width by the height. In this case, the width of the rectangle is the difference between the two time values: (6.0s - 2.0s = 4.0s). The height is the corresponding velocity value at t = 2.0s (v = 8.9 m/s).

Area of rectangle = width * height
Area = 4.0s * 8.9 m/s = 35.6 square meters

2. Triangle:
To find the area of the triangle, you need to multiply the base by the height and divide by 2. The base of the triangle is the same as the width of the rectangle: 4.0s. The height of the triangle is the difference between the two velocity values at t = 2.0s and t = 6.0s (v2 - v1 = 27.6 m/s - 8.9 m/s = 18.7 m/s).

Area of triangle = (base * height) / 2
Area = (4.0s * 18.7 m/s) / 2 = 37.4 square meters

Now, you can add the areas of the rectangle and triangle together to get the total area:

Total area = Area of rectangle + Area of triangle
Total area = 35.6 square meters + 37.4 square meters = 73.0 square meters

Therefore, the area underneath the graph between t = 2.0s and t = 6.0s is 73.0 square meters.

To calculate the distance traveled between t = 2.0s and t = 6.0s, you can use the average velocity formula:

Distance = Average velocity * Time

First, calculate the average velocity between t = 2.0s and t = 6.0s:

Average velocity = (v1 + v2) / 2
Average velocity = (8.9 m/s + 27.6 m/s) / 2
Average velocity = 36.5 m/s

Now, calculate the distance using the average velocity and time interval:

Distance = Average velocity * Time
Distance = 36.5 m/s * (6.0s - 2.0s)
Distance = 36.5 m/s * 4.0s
Distance = 146.0 meters

Therefore, the distance traveled between t = 2.0s and t = 6.0s is 146.0 meters.