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The acceleration is given by the 1st derivative of velocity with respect to time , i.e

a= \frac{dv}{dt}

= \frac{dv}{ds} * \frac{ds}{dt}

= \frac{dv}{ds} *v                        (v= \frac{ds}{dt} )

ds =  \frac{1}{a} *v*dv


 \int\limits^s_0 \, ds =  \int\limits^v_u  \frac{v*dv}{a}

s =  \frac{1}{a} (  \frac{ v^{2} }{2}- \frac{ u^{2} }{2} )

s =  \frac{1}{2a} ( v^{2}- u^{2} )

2as = ( v^{2}- u^{2} )[/tex]

 v^{2} = u^{2} + 2as

This is the third equation of motion.
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