## Frames of Reference

If two objects are moving along the same line but at different speeds, then they will have a relative velocity relative to one another. We can find this by simple addition or subtraction.

The relative speed of car A relative to car B above is 40-30=+10 m/s and the relative speed of car B relative to car A is 30-40=-10 m/s.

In carrying out these calculations we are transforming velocities between three frames of reference.

In a frame of reference stationary relative to the road,

any point on the road has a speed of 0 m/s

car A has a speed of 40 m/s

car B has a speed of 30 m/s

In a frame of reference stationary relative to car A,

any point on the road has a speed of -30 m/s

car A has a speed of 0 m/s

car B has a speed of 10 m/s.

In a frame of reference stationary relative to car B,

any point on the road has a speed of -40 m/s

car A has a speed of -10 m/s

car B has a speed of 0 m/s.

Note that any frame of reference is stationary relative to itself.