Question

explain its derivation please ​

Answer 1

1. v = u + at

We Know,

$a = \frac{v - u}{t} \\ at = v - u \\ v = u + at$

2. $s = ut + \frac{1}{2} a {t}^{2}$

We know,

$avg. \: v = \frac{s}{t} \\ avg. \: v = \frac{u + v}{2}$

Therefore,

$\frac{s}{t} = \frac{u + v}{2} \\ \frac{s}{t} = \frac{u + u + at}{2} \\ \frac{s}{t} = \frac{2u + at}{2} \\ \frac{s}{t} = u + \frac{at}{2} \\ s = ut + \frac{1}{2} a {t}^{2}$

3. v² - u² = 2as

We know,

$t = \frac{at}{a} \\ t = \frac{v - u}{a}$

Now,

$s = avg. \: v \times t \\ s = \frac{u + v}{2} \times \frac{v - u}{a} \\ s = \frac{ {v}^{2} - {u}^{2} }{2a} \\ 2as = {v}^{2} - {u}^{2}$

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