Relative motion is just a way of saying that sometimes different people will say different things about the motion of the same object.

• This is not because one of them is wrong, but because they are using different frames of reference.
• The best way to see how this is possible is to look at some examples.
• In all of the following examples, ignore air resistance.

Example 1: Let’s say I am standing on the back of a pickup truck (that is motionless), and I am throwing apples forwards. I know that I can throw an apple at exactly 15m/s every time.

• If a person were standing on the sidewalk, how fast would she say the apples are moving?
  • Since she will see them exactly the same way as me (we're both in the same reference frame), she will say 15m/s.
• Now the truck starts to move forwards at 20m/s. I am still throwing apples forwards, exactly the same as I was throwing them before, at 15m/s.
  • If I am really not paying attention to what’s going on around me (like the fact that I am standing in the back of a moving truck), how fast would I say the apples are moving?
  • Still 15m/s! Relative to me, I can only make an apple move away from me at 15m/s, so that’s how fast I measure the apple moving away from me.
• How fast does my friend on the sidewalk say the apple is moving?
• Well, even before I throw it, she’ll say that the apple is moving at 20m/s (the speed of everything on the truck).
• When I have thrown the apple forward, adding more velocity to it, she will say it is going at (20m/s + 15m/s) 35m/s!
• Now I turn around and start throwing the apples from the rear of the truck, backwards!
  • I will still say that my apples are moving at 15m/s, because from my way of looking at it, that’s how fast the apple is moving. The only thing I might say that is different is that it is -15m/s, since even I should be able to notice they are going in the opposite direction now.
  • My friend on the sidewalk will say that the apple is moving at (20m/s + -15m/s) 5m/s!

In each of the above examples, we are really talking about two different people having two different frames of reference while measuring the relative velocity of one object.

Frame of reference: When you are standing on the ground, that is your frame of reference. Anything that you see, watch, or measure will be compared to the reference point of the ground. If I am standing in the back of a moving truck, the truck is now my frame of reference and everything will be measured compared to it.

Relative velocity: In the above examples, each person was measuring the velocity of the apples relative to (compared to) the frame of reference that they were standing in. Relative to a person standing on the sidewalk, the apple may be moving at 10m/s, while for a person in the frame of reference of the truck, the apple is moving at 15m/s relative to him.

Example 2: Sitting at your desk, how fast are you moving?

• Relative to the ground: Zero. You’re not moving relative to the frame of reference of the ground.
• Relative to the sun: 2.97e4 m/s! That’s a pretty big difference, but since the Earth is orbiting the sun at this speed, an observer standing on the sun (ouch!) would say that you are moving at 2.97e4 m/s.
• Both of these answers are correct in their own frame of reference.

Example 3: You might have even noticed relative velocity while sitting at a red light…

• Have you ever been sitting at a red light with a bus stopped next to you?
• You’re kind of daydreaming, looking out the window at the side of the bus, when all of a sudden it feels like your car is rolling backwards!
• Then you realize that it was just the bus moving forwards.
  • Your brain knows that the bus was just sitting there on the road… it became part of the frame of reference of the ground.
  • When your brain saw the bus moving forwards, it had already “decided” that the bus won’t move. The only option remaining is that you must be moving backwards.