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

Second Equation of Motion

The second equation of motion connects time, displacement, velocity, and acceleration. The body's displacement is depicted by the region underneath the v-t graph.

s = ut + ½ at²

Step 1: To prove:

v² - u² = 2as

Where

t is the time.

u is initial velocity,

v is final velocity,

a is the acceleration

and s is the displacement,

Step 2: Derivation:

We employ both of the equations of motion to obtain the third equation of motion.

s = ut + ½ at² ….. (1) [Second equation of motion]

v = u + at …. (2) [First equation of motion]

On rearranging we get

t = (v - u)/a

Substitute the value of t in equation (1) s = ut + ½ at²

We get,

s = u (v - u)/a + ½ a (v-u/a)²

2as = 2u (v - u) + (v - u)²

2as = 2uv - 2u² + v² - 2uv + u²

On rearranging we get

2as = v² - u²

v² - u² = 2as

Summary:-

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

The third equation of motion is v² - u² = 2as. It is an equation which connects the final velocity, initial velocity, acceleration and distance.

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