| The Rules: 1. Everything must be done with differences or scaled differences. 2. Scalars are numbers which are either real numbers or complex numbers. 3. A scalar never exists by itself, it is always attached to a difference. Regarding Rule 3, if you want to scale a ratio of differences you can put the scalar on the difference in the numerator and you get what you want. |
| Hints 1. Anything you see in a physics textbook that has a  symbol in front of it qualifies as a difference.2. Anything you see in a physics textbook that has a  symbol or  symbol in front of it also qualifies as a difference.3 If you see an arrow over a variable, like  it qualifies as one of our differences.4. When you find a physics equation should expect to find: (a) a change on one side and a change on the other. (b) a ratio of changes being equal to a constant. This part gets tricky though, that constant may change as we change a coordinate. |
Overview
A change in position requires a velocity. How much change of distance we get for a given change of time depends on the velocity.
A change in velocity requires an acceleration. How much change of velocity we get for a given change of time depends on acceleration.
A force is required to cause an acceleration. How much acceleration we get from a given force depends on mass.
Displacement
For our example we will judge position by mile markers on a highway.
A displacement is the difference between two locations, an initial location and a final location. The trip from mile marker 101 to mile marker 107 is a displacement of 6 miles.
For our example we are traveling in a 1D space and we are calling it the x-axis.
Our trip is a vector and we get this vector by multiplying “mile in the positive x-direction” by the number 6.
Time Interval
We see a time interval as something that does to time what displacement did to position. The time interval of two hours is two hours regardless of if it started at 8:15 and ended at 10:15 or if it started at 2 PM and ended at 4 PM.
Velocity
Velocity is a displacement divided by a time interval. We have previously recognized these two quantities so we can say velocity is a ratio of recognized quantities.
Velocity as we calculate it is called “Average Velocity” elsewhere. You might see the odometer change by 180 miles over a time interval of 3 hours and you calculate a velocity of 60 miles per hour. The idea that it is just an average velocity acknowledges that you drove 65 to 70 miles per hour all the time you were driving but you were driving 0 mph while you were stopped for gas or to get food.
Acceleration
Acceleration is a change of velocity divided by a time interval. It fits our criterium of being a difference.
Later, we will deal with issues that come up, issues that suggest our strategy needs further refinement. We offer a vague hint, the increase of difficulty going from Special Relativity to General Relativity comes the curvature to spacetime caused by gravity. Gravity and Acceleration are mathematically linked.
Force
Mass
Vectoreverything 