Question

explain third eqution of motion

Answer 1

v2 = u2 + 2aS

where,

v = final velocity,

S = displacement,

u = initial velocity,

a = acceleration (must be constant),

This equation DOES NOT relate to final velocity.

Analytical Proof

We know that,

a = dvdt

v = dSdt

Taking their ratio, we get,

av = dvdS

Hence,

a = vdvdS

Cross multiplying ‘dS’ and integrating both sides,

S∫0 a . dS = v∫u v . dv ⇒ aS = v2 - u22

v2 = u2 + 2aS


hope this helps