a We have a ball rolling down a ramp. Our ramp is 12 feet long and we marked 6 distances equally spaced 2 feet apart.
We will measure the distance d and the time t it takes a ball to roll from each mark to the bottom of the ramp. Depending on the lengths between the markings and the angle between the ramp and the ground, there will be variations in the data sets. For this case, we have the following data set.
d
t
2
0.5
4
≈ 0.7
6
≈ 0.9
8
1
10
≈ 1.1
12
≈ 1.2
Now, let's plot these ordered points and connect them with a smooth curve.
Extra
Why does the graph have this shape?
When a ball goes down a ramp, the speed gradually increases. This is because the force of gravity exerted on an object increases the downward speed by 3.2 feet per second. This change causes the ball to gain momentum every second. As a result, the rate of motion also increases. This is why the distance grows faster as time passes.
b From the graph that we drew in the Part A, we can see that the curve gradually stops increasing at some point. This behavior resembles graphs from the square root function family. To show this, let's compare our curve with an example function from this family.
We can see that both curves have similar shapes. Therefore, our function is also a square root function.
c We want to know if the graph of the distance is linear. To do so, recall that a linear function is a polynomial of degree zero or one. Also, remember that all linear functions are straight lines.
With this information, we can conclude that our graph is not linear.
