Question

Work out the distance between the 2 stops

Answer 1

a.
`(7)/(20) (m)/(s^2)`

b. 945 m

c. 5.9 m/s

Explanation:

a. Since we are looking at a velocity graph, acceleration is equal to it's derivative, or slope. To find the slope here, we can just use the slope equation:

`a = (y_2 - y_1)/(x_2 - x_1) = (7 - 0)/(20 - 0) = (7)/(20)`

b. To find the distance between the stops, we can find the area under the graph, which is equal to the distance covered. To do this, we can separate the graph into three parts, the two triangles on the end, and the rectangle in the middle.

For the first triangle, to find the area, we use
`a = (1)/(2)(bh)`. The base will be 20s - 0s and the height will be 7m/s - 0m/s

Plugging this in gives us:

`a = (1)/(2)(20 * 7) = 70`

For the rectangle, we can find area using just the height and base, the base being 130s - 20s and the height being 7m/s - 0m/s

The equation would then be, a = (130 - 20) * (7 - 0) = 110 * 7 = 770

For the last triangle, we will use the triangle area formula, with the base being 160s - 130s and the height being 7m/s - 0m/s

Plugging this in gives us:

`a = (1)/(2)((160 - 130) * (7 - 0)) = (1)/(2)(30 * 7) = 105`

Then add the values together: 70 + 770 + 105 = 945 m

c. To find average velocity, we divide the total distance (945) by the total time (160):

`(945)/(160) = 5.90625`

Rounded to 1 d.p. becomes 5.9 m/s

Hope this helps, if you need anything explained please let me know.