Question

please derive V^2=u^2+2as numerically​

Answer 1

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

$v = u + at \: (from \: \: 1)$

Taking the square of both side

$v ^{2} = (u + at) ^{2}$

$v ^{2} = {u}^{2} + {at}^{2} + 2uat$

${v}^{2} = {u}^{2} + {a}^{2} {t}^{2} + 2uat$

${v}^{2} = {u}^{2} + \frac{2}{2} {a}^{2} {t}^{2} + 2uat$

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

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

Answer 2

Answer:

2av

2

=u

2

+2a

v = u + at \: (from \: \: 1)v=u+at(from1)

Taking the square of both side

\begin{lgathered}v ^{2} = (u + at) ^{2} \\\end{lgathered}

v

2

=(u+at)

2

v ^{2} = {u}^{2} + {at}^{2} + 2uatv

2

=u

2

+at

2

+2uat

{v}^{2} = {u}^{2} + {a}^{2} {t}^{2} + 2uatv

2

=u

2

+a

2

t

2

+2uat

{v}^{2} = {u}^{2} + \frac{2}{2} {a}^{2} {t}^{2} + 2uatv

2

=u

2

+

2

2

a

2

t

2

+2uat

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

2

=u

2

+2a(

2

1

at

2

+ut)

{v}^{2} = {u}^{2} + 2asv

2

=u

2

+2as

Explanation:

2av

2

=u

2

+2a

v = u + at \: (from \: \: 1)v=u+at(from1)

Taking the square of both side

\begin{lgathered}v ^{2} = (u + at) ^{2} \\\end{lgathered}

v

2

=(u+at)

2

v ^{2} = {u}^{2} + {at}^{2} + 2uatv

2

=u

2

+at

2

+2uat

{v}^{2} = {u}^{2} + {a}^{2} {t}^{2} + 2uatv

2

=u

2

+a

2

t

2

+2uat

{v}^{2} = {u}^{2} + \frac{2}{2} {a}^{2} {t}^{2} + 2uatv

2

=u

2

+

2

2

a

2

t

2

+2uat

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

2

=u

2

+2a(

2

1

at

2

+ut)

{v}^{2} = {u}^{2} + 2asv

2

=u

2

+2as