Question

what is the formula third equation of motion?write the formula and prove that.

Answer 1

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 = $\frac{1}{a} *v*dv$

Therefore,

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

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.