Equations of Motion
The following methods can be used to obtain the equations of motion:
- By Graphical Method
- By Calculus Method
- By Simple Algebraic Method
Third Equation of Motion
We need to demonstrate the third motion equation.
The third Equation of Motion states that:
v2 - u2 = 2as
Proof -
- Let initial speed = u
- Acceleration = a
- Final speed = v
- Time = t
From the first equation of motion we have
v = u + at
On rearranging we get
or t = (v - u)/a
Average velocity is given as (v + u)/2
Also, we know that
Distance = average velocity X Time
s = (v + u)/2 x (v - u)/a
After solving
We get
v2 - u2 = 2as
This is the third equation of motion.
Summary:
Derive Third Equation of Motion.
The third equation of motion is v2 - u2 = 2as. The equation of motion can be determined using calculus, graphical and simple algebraic methods.
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