Question

If you were to look at 2 graphs, and one had a linear plot and the other was a bit more scattered, what does the fact that the graph is linear say about the acceleration of an object compared to the other?

Comparing the 2 graphs, they both have the same y axis in meters except different t in seconds on the x axis- one of the graphs has normal t values, and the other graph is the exact same except the t values are now squared. The graph with the normal t values is a bit more scattered than the graph with the squared t values, which forms a linear line.

Also, can acceleration be found from these graphs using mx+b formula (using the m value)?

Answer 1

Yes, the information you gave pertains to a graph of simple pendulum. When we plot L vs T graph , the data is more scattered as it leads to more uncertainty when we draw a linear fit.

On the other hand, when we use T² , the get becomes more linear with change in length. This can be understood by looking at the following equation

If we square both sides, we get

so,

g (which is also the acceleration which you intend to find) can be calculated as