Chapter 1: Linear motion

The object is moving along a straight line with no curvature in its path, like driving a car in Corvallis downtown, third street.

Linear motion is kind of driving in Corvallis downtown, 3rd street.

We want to find a mathematical equation that is short, and accurate enough to describe any linear motion. Let’s start with the most simplest motion, moving with a constant speed. Like driving in a highway at a constant speed.

Linear motion with a constant speed

For this category of motion (let’s call it, linear motion with a constant speed) there is an equation (mathematical model) that connects “the distance between initial and final location”, “the object speed between the initial and final location”, and “the time it takes to go from the initial to final location”. In words, this equation is:

“the distance between initial and final location” = “the object speed between the initial and final location” times “the time it takes to go from the initial to final location”

Example 1

Let’s practice how to use this equation for a simple case, imagine you are driving your car with a constant speed of 65 miles per hour in I-5 from Albany, OR to PDX airport and it will take one hour for you to get there, so you know two out of the three variables of the equation. Then you can calculate the last one, “the distance between Albany, OR and PDX”. In this case, it will be 65 miles.


Chapter 0: Mathematics background


“A unit is a standard measure of a quantity in science”. Before 18th century, around the world, science communities based on the history of science in their location had their own standard units of measurement. In 19th century, by development of roads and communication systems, scientist came together to pick a standard system of measurement to be able to share their knowledge in a common language. Without any doubt, it was not easy at the beginning but finally after a long period of arguments “System International” (french word) know as “metric system” or “SI” became the world standard system of measurement.

Now the question is when we need to use a unit. Well, anything that we measure needs a unit. Literally there is only one category for variables that don’t have a unit in whole science when we measure them, and that is when we count number of something. For example, Julia is checking a sample under a microscope in a biophysics lab. The following picture is what she is looking at,

Juan: “Julia, how many cells do you see in the red contour?”

Julia: “I see four cells.”

As you see, Julia is measuring number of the cells in the red contour but she didn’t use any unit to report it.

Another example, Juan is measuring the weight of her samples in the lab on a scale. The following picture shows what scale reads,


Metric prefixes

Scalar vs. vector