Depending on the frame of reference, the same motion can be described in different ways. Watch the following video of a car circling a track at the Paris Motor Show.

1. As you stand next to a road, a car passes you moving at 20 m/s to the north. Describe how the stated scenario would look in the eyes of the passenger inside the car.

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   The passenger thinks of himself as sitting still and sees you as moving at 20 m/s to the south.

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The motion does not change, just the point of view of the observer; one person is sitting in a moving frame of reference. What if both reference frames are moving? Watch the following video of a golf turbo test camera onboard a car.

Source: Golf Turbo Test camera onboard, aphael Zamora, YouTube

2. You are driving 30 m/s to the east, and you pass another car that is moving 20 m/s to the east. How would the stated scenario look from the point of reference from each car?

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   The driver of the car that you pass sees you as moving 10 m/s to the east, but you see him or her moving 10 m/s to the west.

If you look at this mathematically, you can write the equation as v_A − v_B = v_rel. In the example above, 30 − 20 = 10, so v_rel = 10 m/s. If the cars were moving in opposite directions, the velocities would be 30 m/s east and 20 m/s west. The relative velocity would be 30 − (-20) = 50 m/s. Since one car is moving 20 m/s west or in the opposite direction, we can think of the velocity as -20 m/s.

The general rule to find the magnitude of the relative velocity between two cars is as follows:

• If the cars drive toward each other or away from each other, then you add their speeds.
• If the cars are moving the same direction, then you subtract their speeds.