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

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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.

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.

##### 1 Answer

Gradient: Force

Y-Intercept: Systematic Error

#### Explanation:

The gradient of a graph is

Which is equal to Force (

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

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.