# What do the slope and intercept represent in a Mass vs 1/acceleration graph?

## I have run a cart+fence along a level air track. I have been told to make the graph shown here of mass against reciprocal acceleration. What is the significance of the m/a slope, and what is the significance of the intercept? The equation in the legend is of the trendline for these data. Sep 26, 2017

Y-Intercept: Systematic Error

#### Explanation:

The gradient of a graph is $\text{rise" / "run}$, $\frac{\delta y}{\delta x}$, so in this case your y-axis variable is mass (m) and your x-axis variable is inverse acceleration ($\frac{1}{a}$) , so substitute these into the equation for the gradient of a straight line.

$\frac{m}{\frac{1}{a}}$, which is the same as $m \div \frac{1}{a}$, to do this we multiply be the reciprocal so $m \times a$.

Which is equal to Force ($F = m a$)

So the gradient represents the constant force applied.

A y-intercept occurs when there is a error that applies to all tests (systematic error). This is because our equation $F = m a$ has no constant added onto the end meaning the graph should pass through (0,0).

In this case you have a small positive y-intercept.

This could have been caused by a range of errors when conducting the experiment. A few possible ideas are an extra force applied to hold the cart in place which could be due to the ramp being on a slight slope, holding the cart with your hand. The error could have also be used by the scale being calibrated incorrectly, you measuring the mass incorrectly.

There are a range of possibilities that could cause the intercept. I suggest thinking of something that affected all tests and using that as a reason.