We know that,
[tex] \bf \: v = u + at \: [/tex]
[tex] \red{ \bf \: u = \: v - at \: \: \: \: \: \: ... \: (1)}[/tex]
[tex] \red{ \bf \: s = ut + \dfrac{1}{2} \: at {}^{2} \: \: \: \: ...(2) }[/tex]
[tex] \implies \: \bf \: s = (v - at)t \: + \dfrac{1}{2} at {}^{2} [/tex]
[tex] \implies \: \bf \: s = vt - at {}^{2} \: + \dfrac{1}{2} at {}^{2} [/tex]
[tex] \implies \: \bf \: s = vt + \dfrac{ - 2at {}^{2} + at {}^{2} }{2} [/tex]
[tex] \implies \: \bf \: s = vt + \dfrac{ - at {}^{2} }{2} [/tex]
[tex] \implies \: \bf \: s = vt - \dfrac{ at {}^{2} }{2} [/tex]
[tex] \implies \: \bf \: s = vt - \dfrac{1}{2} at {}^{2} [/tex]
[tex]\therefore\sf\red{ \underline{\:The \: given \: statement \: is \: true \: ...}}[/tex]
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Verified answer
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
[tex] \bf \: v = u + at \: [/tex]
[tex] \red{ \bf \: u = \: v - at \: \: \: \: \: \: ... \: (1)}[/tex]
[tex] \red{ \bf \: s = ut + \dfrac{1}{2} \: at {}^{2} \: \: \: \: ...(2) }[/tex]
Substituting value of eq-(1) in eq-2
[tex] \implies \: \bf \: s = (v - at)t \: + \dfrac{1}{2} at {}^{2} [/tex]
[tex] \implies \: \bf \: s = vt - at {}^{2} \: + \dfrac{1}{2} at {}^{2} [/tex]
[tex] \implies \: \bf \: s = vt + \dfrac{ - 2at {}^{2} + at {}^{2} }{2} [/tex]
[tex] \implies \: \bf \: s = vt + \dfrac{ - at {}^{2} }{2} [/tex]
[tex] \implies \: \bf \: s = vt - \dfrac{ at {}^{2} }{2} [/tex]
[tex] \implies \: \bf \: s = vt - \dfrac{1}{2} at {}^{2} [/tex]
Hence, proved !
[tex]\therefore\sf\red{ \underline{\:The \: given \: statement \: is \: true \: ...}}[/tex]
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