Mathematical Development of Linear Motion Equations

Starting Point:

>>>The equation of motion (v2 = v1 + at) developed in the previous section is really a linear equation of the form:  y = mx + b

m is the slope of the line, and b is the y-intercept

Using our kinematics symbols we can redefine the above relationship as follows:

y = mx + b  is a liner function (a straight line) of  v(t); "velocity as a function of time" in a distance-time graph

recalling from previous knowledge


In a velocity-time graph, this becomes:

More specifically:


Using equations 1 and 2 we can obtain a

The above equation can also be written as d = v1t + 1/2 at2

Another useful equation can be derived as follows:

we start with our very first equation  vav = d/t
Where vav is the average velocity, d is the total distance and t the total time.

We can also express the average velocity as vav = (v1 + v2)/2 


Summary of the Five Essential Linear Motion Equations