Question

Direve equation v2-u2=2as by graphical method

Answer 1

$\overbrace{\underbrace{\sf{★Answer★}}}$

As per the lows of motion we know that,

• S = ut + 1/2 at²
• v = u + at

Now, we rearrange the first equation to get

$t=\frac{v–u}{t}$

We can use this to replace t wherever it appears in the second equation. So

$s = ut + \frac{1}{2} \: at^{2} \\ \\ s = u \: ( \frac{v - u}{a} ) + \frac{1}{2} \: a \: ( \frac{v - u}{a} ) ^{2} \\ \\ 2as \: = 2u \: (v - u) + (v - u)^{2} \\ \\ 2as \: = 2uv - 2u ^{2} + v ^{2} - 2uv + u ^{2} \\ \\ 2as \: = \: v^{2} - \: u^{2} \\ \\ v ^{2} = u^{2} + \: 2as$

Hence proved........

Answer 2

Answer:

$As \: \: per \: \: the \: lows \: \: of \: \: motion \: \: we \: \: know \: that,</p><p></p><p>S = ut + 1/2 at²As per the lows of motion we know that,</p><p></p><p>S = ut + 1/2 at²</p><p></p><p>v = u + at</p><p></p><p>Now, we rearrange the first equation to get</p><p></p><p>t=\frac{v–u}{t}t=tv–u</p><p></p><p>We can use this to replace t wherever it appears in the second equation. So</p><p></p><p>\begin{gathered}s = ut + \frac{1}{2} \: at^{2} \\ \\ s = u \: ( \frac{v - u}{a} ) + \frac{1}{2} \: a \: ( \frac{v - u}{a} ) ^{2} \\ \\ 2as \: = 2u \: (v - u) + (v - u)^{2} \\ \\ 2as \: = 2uv - 2u ^{2} + v ^{2} - 2uv + u ^{2} \\ \\ 2as \: = \: v^{2} - \: u^{2} \\ \\ v ^{2} = u^{2} + \: 2as\end{gathered}s=ut+21at2s=u(av−u)+21a(av−u)22as=2u(v−u)+(v−u)22as=2uv−2u2+v2−2uv+u22as=v2−u2v2=u2+2as</p><p></p><p></p><p></p><p></p><p>v = u + at</p><p></p><p>Now, we rearrange the first equation to get</p><p></p><p>t=\frac{v–u}{t}t=tv–u</p><p></p><p>We \: can \: use \: this to replace t wherever it appears in the second equation. So</p><p></p><p>\begin{gathered}s = ut + \frac{1}{2} \: at^{2} \\ \\ s = u \: ( \frac{v - u}{a} ) + \frac{1}{2} \: a \: ( \frac{v - u}{a} ) ^{2} \\ \\ 2as \: = 2u \: (v - u) + (v - u)^{2} \\ \\ 2as \: = 2uv - 2u ^{2} + v ^{2} - 2uv + u ^{2} \\ \\ 2as \: = \: v^{2} - \: u^{2} \\ \\ v ^{2} = u^{2} + \: 2as\end{gathered}s=ut+21at2s=u(av−u)+21a(av−u)22as=2u(v−u)+(v−u)22as=2uv−2u2+v2−2uv+u22as=v2−u2v2=u2+2as</p><p></p><p></p><p>$