Third equation of Motion The first equation of motion is v = u + at.

Third equation of Motion The first equation of motion is v = u + at.

v - u = at ... (1)

Average velocity = st ... (2)

Average velocity = u+v2 ... (3)
From equation (2) and equation (3) we get,

u+v2 = st ... (4)

Multiplying eq (1) and eq (4) we get,

(v - u)(v + u) = at x 2st

(v - u)(v + u) = 2as

[We make use of the identity a² - b² = (a + b) (a - b)]
 v² - u² = 2as.......................... Third equation of motion.