Derive the third equation of motion graphically.

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Solution

Consider the velocity-time graph of a body moving with uniform acceleration 'a'.

Distance travelled in time t, $s = \frac{(O A + B C) \times O C}{2}$
$= \frac{(u + v) \times t}{2}$
From the first equation of motion, $t = \frac{(v - u)}{a}$
Substituting we get, $s = \frac{(v + u) \times (v - u)}{2 a} \Rightarrow 2 a s = v^{2} - u^{2}$

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