Question

diverse the formula
1. v=u-at
2.s = ut+1/2 at*t
3. v*v=u*u + 2as​

Answer 1

Explanation:

Derive :

$v = u + at$

Ans:

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

Derive :

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

Ans:

In general ,

S=vt

But if acceleration isn't constant then,

$s = v_{avg}t$

And,

$v _{avg} = \frac{v + u}{2}$

Hence,

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

Derive:

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

Ans:

$v = u + at \\ {v}^{2} =( {u + at})^{2} \\ {v}^{2} = {u}^{2} + {a}^{2} {t}^{2} + 2uat \\ = {u}^{2} + 2a(ut + \frac{1}{2} a {t}^{2} ) \\ {v}^{2} = {u}^{2} + 2as$

Hence proved...