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Derive the Third Equation of Motion: v2 – u2 = 2as

Answer: Kinematics equations represent the fundamental idea of object motion, like the position, velocity, and acceleration of an item at different intervals. The motion of such an item in 1D, 2D, and 3D is governed by 3 equations. Among the most significant concepts in Physics is the derivation of such laws of motion. 

v2 = u2 + 2as is the third equation of motion.

We already know that v = u + at = t = (v-u)/a or v-u = at

We already remember that distance equals average velocity multiplied by time.

Therefore, s = [(v+u)/2] X [(v-u)/a]

s = (v2 – u2)/2a

2as = v2 – u2 or v2 = u2 + 2as.

The link between the particle’s final velocity v, starting velocity u, constant speed a, with displacement S is the 3rd equation of motion. To use the equations of motion established previously, we can now determine the movement of particles during the n-th second.