Is it good or bad?
In the graph of “x position vs. time”, we can find the velocity of the basketball by using the “Linear Fit” tool. When we click on this tool’s button, a dialogue box pops up (see graph on next page), which says the slope m is equal to 3.039 m/s. This is the velocity of the basketball in the x-direction, since the slope of the x position versus time graph gives us the x-direction velocity of the basketball. In other words, the velocity in the x-direction, vx ,is given by
On a graph of x vs. t, the slope is found by measuring Δx/Δt: how much the line changes in position x (change along the vertical axis of the graph) divided by how much the line changes in time t (change along the horizontal axis of the graph).
From the Linear Fit dialogue box, the correlation is given as 1.000. This is measuring the correlation coefficient, which quantifies the degree to which two variables are related. The correlation coefficient measures how much one variable changes when another one does. In our case, the correlation coefficient is measuring how much the position x variable changes as the time t variable changes.
The value of the correlation coefficient ranges from -1 to 1. If the correlation coefficient measures 0, then there is no relationship between the two variables. If the correlation coefficient is positive, then one variable goes up as the other variable goes up. If the correlation coefficient is negative, then one variable is going down as the other variable goes up. The correlation coefficient is the same if you swap the order of the variables you are considering.
If the correlation coefficient measures 1, then the two variables are maximally correlated. What this means in our case, is that the position x and the time t are maximally correlated, in other words, there is a strong relationship between them so that if one goes up the other will do the same. This measurement result of 1 for