How can motion appear different from different obserers

One of the main concepts in physics is the idea that motion is relative to the observer. Think about it this way: when you're driving in a car and you look out the window, you see a person standing on the side of the road. You may know that the car you're driving is in fact what is in motion, but it looks like the person is moving because of your perspective.

On the other hand, if you're standing on the side of the road and you see a car speeding by you, the car appears to be the one in motion, not you.

It is for this reason that when you're setting up motion equations and similar stuff that you can make the acceleration in any direction you want, as long as things like the position and the velocity stay relative to that acceleration.