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Question

Derive the third equation of motion:v2-u2=2as.


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Solution

Step 1: To prove:

v2-u2=2as

Where u is initial velocity, v is final velocity, a is the acceleration and s is the displacement, t is the time.

Step 2: Derivation:

For getting the third equation of motion, we use both of the equations of motion

S=ut+12at2__________(1)(2ndequationofmotion)v=u+at_____________(2)(1stequationofmotion)t=(vu)/a

Substitute the value of t in equation (1),S=ut+1/2at2,

We get,

S=u(v-ua)+12a(v-ua)2

2aS=2u(vu)+(vu)22aS=2uv2u2+v22uv+u22aS=v2u2v2-u2=2as

Hence, v2-u2=2as


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