Find out the answer to "Derive the third equation of motion:v2-u2=2as."

Charlize Garza

Answered question

2023-02-01

Derive the third equation of motion:

v^{2} - u^{2} = 2 a s

Answer & Explanation

usifaneledv2

Beginner2023-02-02Added 10 answers

To prove:

v^{2} - u^{2} = 2 a s

A is the acceleration, s is the displacement, u is the initial velocity, v is the final velocity, and t is the time.
Derivation:
For getting the third equation of motion, we use both of the equations of motion

S = u t + \frac{1}{2} a t^{2}__________(1) (2 n d e q u a t i o n o f m o t i o n) v = u + a t_____________(2) (1 s t e q u a t i o n o f m o t i o n) t = (v - u) / a

Substitute the value of t in equation (1),

S = u t + 1 / 2 a t^{2}

,
We get,

S = u (\frac{v - u}{a}) + \frac{1}{2} a {(\frac{v - u}{a})}^{2}

\Rightarrow 2 a S = 2 u (v - u) + {(v - u)}^{2} \Rightarrow 2 a S = 2 u v - 2 u^{2} + v^{2} - 2 u v + u^{2} \Rightarrow 2 a S = v^{2} - u^{2} \Rightarrow v^{2} - u^{2} = 2 a s

Hence,

v^{2} - u^{2} = 2 a s

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Derive the third equation of motion: v^2-u^2=2as

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