hypothesis about a graph of avg acc vs. slope being linear?

Question

● the ramp is 70 cm long @ various slopes.
● time required to travel 70 cm, various at the different slopes.
○ slope 1 = 3 seconds
○ slope 2 = 2 seconds
○ slope 3 = 1.8 seconds
The difference in elevation for the slopes are
○ slope 1 is elevated 2.1 cm
○ slope 2 is elevated 3.8 cm
○ slope 3 is elevated 5.3 cm

Does the previous info support the idea that a graph of avg acc vs slope will be linear?

Answer 1

The acceleration on the slope is related to the elevation of the slope as
sin(theta)=elevation/L

The acceleration down the slope is related to theta as

a*sin(theta)

The time to travel down the slope is related to L as

L=.5*sin(theta)*a*t^2

or

L=.5*a*t^2*elevation/L

2*L^2/(elevation*t^2)=a

a is inversely proportional to elevation
which is a linear relationship


j

Answer 2

Well if you are taking the avg acceleration over the entire length of the test then by definition it will be linear (by taking the average you remove all the variation and take the mean of the different accelerations over the entire test).