### Mathematical Development of Linear Motion Equations

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__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

Where::

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 = v _{1}t + 1/2 at^{2}**

Another useful equation can be derived as follows:

we start with our very first equation v_{av }= 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 **

Therefore,

#### Summary of the Five Essential Linear Motion Equations

1 | ||

2 | ||

3 | ||

4 | ||

5 |