Question

if we substitute the equation u= v-at we get s = vt - 1/2 at². is it true or false... ​

Answer 1

Given statement is true .

s = vt - ½ at²

Proof :

We know that,

♣First equation of motion:- v= u + at

♣Second equation of motion s= ut + 1/2 at²

$\bf \: v = u + at \:$

$\red{ \bf \: u = \: v - at \: \: \: \: \: \: ... \: (1)}$

$\red{ \bf \: s = ut + \dfrac{1}{2} \: at {}^{2} \: \: \: \: ...(2) }$

Substituting value of eq-(1) in eq-2

$\implies \: \bf \: s = (v - at)t \: + \dfrac{1}{2} at {}^{2}$

$\implies \: \bf \: s = vt - at {}^{2} \: + \dfrac{1}{2} at {}^{2}$

$\implies \: \bf \: s = vt + \dfrac{ - 2at {}^{2} + at {}^{2} }{2}$

$\implies \: \bf \: s = vt + \dfrac{ - at {}^{2} }{2}$

$\implies \: \bf \: s = vt - \dfrac{ at {}^{2} }{2}$

$\implies \: \bf \: s = vt - \dfrac{1}{2} at {}^{2}$

Hence, proved !

$\therefore\sf\red{ \underline{\:The \: given \: statement \: is \: true \: ...}}$

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