# Metric for movement in 2D space

I have a set of points that represent the coordinates of an object moving in the 2D space at different points in time.

Using this points I want to get a "measurement" that will describe the general movement of the object.

My initial try was to compute the instantaneous velocity vectors at each point in time and then average the vectors to get the average velocity vector.

My second attempt was to apply linear regression and use the slope of the resulting line and the average speed to compute an average velocity vector. The problem I'm facing here is that I don't know how to compute the average velocity vector using the average speed and the the slope of the linear regression line.

I also need an opinion on which method is better or if there is a better way of achieving what I want.

• The average velocity of a particle over some time interval is just (position at end of interval - position at start of interval)/(duration of interval). – Rahul Jul 13 '14 at 17:30
• @Rahul I know that that is the textbook definition for the average velocity vector. I was doing it the way I described it to try to take advantage of the extra information I have about the object's movement – John Retallack Jul 13 '14 at 17:56