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Updated: 13 Jun 2026, 12:22:16

E=mc^2

First Equation of Motion

Given:

Initial velocity = u
Final velocity = v
Acceleration = a
Time = t

Formula:

v = u + at

Second Equation of Motion

Distance travelled in time t:

s = ut + (1/2)at^2

Third Equation of Motion

Formula:

v^2 = u^2 + 2as

Derivation of the Third Equation

From the first equation:

v = u + at

Therefore,

t = (v - u)/a

Substitute into the second equation:

s = u[(v - u)/a] + (1/2)a[(v - u)/a]^2

Simplifying:

s = (uv - u^2)/a + (v - u)^2/(2a)

Multiplying both sides by 2a:

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

Expanding:

2as = 2uv - 2u^2 + v^2 - 2uv + u^2

2as = v^2 - u^2

Therefore,

v^2 = u^2 + 2as

All Three Equations Together

v = u + at

s = ut + (1/2)at^2

v^2 = u^2 + 2as

These are commonly called Newton's equations (or equations of uniformly accelerated motion). The powers are written in the form you requested, such as v^2, u^2, and t^2.

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Swarnim Raj

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Experienced education and career writer at Infokept Career Hub, creating simple, research-based guides for students and government job aspirants.

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