Question

prove
v²=U²+2as by normal method​

Answer 1

Answer:

[ V = u + at { equation 1 from } ; t = v - u /a

& Put the t value in equation 2 , i.e.,

S = ut + 1/2 at^2

S = u ( v - u ) /a + 1/2 a { ( v - u ) /a } ^2

S = v - u /a [ u + 1/2 a { v - u /a }

S = v - u / a . ( v + u / 2 ) [ by cancelling above step }

S = v^2 - u^2 /2a

2as = v^2 - u^2 / v^2 = u^2 + 2as

Hope !! It helps ..

Explanation:

Answer 2

Explanation:

Here, we are asked to derive the third equation of motion, that is v² = u² + 2as.

As we know that according to the first and second equation of motion,

• $\rm {v = u + at} \dots \bf{(1)}$

• $\rm {s = ut+ \dfrac{1}{2}at^2} \dots \bf{(2)}$

In the first equation of motion, we have :

$\longmapsto \rm {v = u + at}$

Or, we can write it as,

$\longmapsto \rm {v -u = at }$

$\longmapsto \rm {\dfrac{v -u }{a} =t \quad \dots \bf{(1)} }$

Now, substitute the value of t from equation (1) into the equation (2).

$\longmapsto\rm {s = ut +\dfrac{1}{2}at^2}$

$\longmapsto\rm {s = u\Bigg (\dfrac{v -u }{a} \Bigg ) + \dfrac{1}{2}a{\Bigg (\dfrac{v -u }{a} \Bigg )}^2}$

$\longmapsto\rm {s = \dfrac{u(v -u) }{a} + \dfrac{a}{2} \Bigg ( \dfrac{v^2 + u^2 -2vu}{a^2} \Bigg) }$

$\longmapsto\rm {s = \dfrac{u(v -u) }{a} + \dfrac{a(v^2 + u^2 -2vu)}{2(a^2)} }$

$\longmapsto\rm {s = \dfrac{uv - u^2 }{a} + \dfrac{\cancel{a}(v^2 + u^2 -2vu)}{2\cancel{a^2}} }$

$\longmapsto\rm {s = \dfrac{uv - u^2 }{a} + \dfrac{(v^2 + u^2 -2vu)}{2a} }$

$\longmapsto\rm {s = \dfrac{\cancel{2uv} - 2u^2 + v^2 + u^2 \cancel{-2vu}}{2a} }$

$\longmapsto\rm {s = \dfrac{-2u^2 + v^2 + u^2}{2a} }$

$\longmapsto\rm {s = \dfrac{v^2 - u^2}{2a} }$

$\longmapsto\rm {2as = v^2 - u^2}$

$\longmapsto\bf {2as + u^2 = v^2 }$

Hence, proved!

More Information :

Equations of motion :

$\boxed{ \begin{array}{cc} \pmb{\sf{ \quad \: v = u + at \quad}} \\ \\ \pmb{\sf{ \quad \: s= ut + \cfrac{1}{2}a{t}^{2} \quad \: } } \\ \\ \pmb{\sf{ \quad \: {v}^{2} - {u}^{2} = 2as \quad \:}}\end{array}}$

• v denotes final velocity
• u denotes initial velocity
• a denotes acceleration
• t denotes time
• s denotes distance