Saturday, February 18, 2006

Motion Tracking

Finding position as a function of time

Suppose a particle goes from x1 to x3 and then back to x2 at times t1, t2 and t3 respectively. (figure 1)

We can plot where the particle is at different times on a graph (figure 2).

If we also measure the position of the particle at many intermediate times, we can fill in this curve, referred to x(t) – x as a function of time. (figure 3)

Following are some examples:

1) This is a straight line plot – in any time period Deltat, the Deltax is proportional to Deltat. v= Deltax/Deltat is positive with a constant value.

2) This plot also shows a particle with a positive constant velocity. However, because this plot has a steeper slope, the particle has a higher velocity – it is going faster.

3) This plot has a downwards slope – it describes a particle moving in the negative direction.

4) This plot is horizontal. The particle it describes is not moving at all.

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