Question

how third equation of motion is derived​

Answer 1

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Newton third law of motion describes for every reaction there is equal and opposite reaction.

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Answer 2

3rd equation of motion derivation:

Solving for a body under constant acceleration, for a displacement 0 to s,

(initial velocity=u, final velocity=v)

a = dV/dT

multiply divide by dS

a= dV/dS * dS/dT

dS/dT is equal to velocity ( rate of change of displacement)

a= dV/dS * V

a*dS = V*dV

Integrate both sides

(P.S: integreal signs as well as limits aren't possible in the keyboard)

(Integral x = x^2/2)

(a constant)

(Integral dS = s)

[V^2/2] (limit u to v) = a [S] (limit 0 to s)

V^2/2 — U^2/2 = a ( s-0)

V^2 — U^2 = 2as

V^2 = U^2 + 2a