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
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 = 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
Therefore,
Summary of the Five Essential Linear Motion Equations
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2 | ||
3 | ||
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5 |