Question

v^2=u^2+2as prove this mathematical

Answer 1

Answer:

Here, we are using two formulas :

• v = u + at, and,

• s = ut + $\frac{}{} \frac{1}{2}$ a$t^{2}$;

We simply equate them, and get the answer.

Step-by-step explanation:

By mathematical equation, we solve it like this :

v = u + at

v - u = at

$\frac{v - u}{a}$ = t; or; t = $\frac{v - u}{a}$ --------- Eqn. 1

s = ut + $\frac{}{} \frac{1}{2}$ a$t^{2}$

By replacing the value of 't', from Eqn. 1, we get,

s = $\frac{u(v - u)}{a}$ + $\frac{1}{2}$ $\frac{a(v - u)^{2} }{a^{2} }$

s = $\frac{uv - u^{2} }{a}$ + $\frac{1}{2}$ $\frac{v^{2} - 2vu + u^{2}}{a} }$

s =  $\frac{uv - u^{2} }{a}$ + $\frac{v^{2} - 2vu + u^{2}}{2a} }$

s = $\frac{2(uv - u^{2}) + v^{2} - 2uv + u^{2} }{2a}$

s = $\frac{2uv - 2u^{2} + v^{2} - 2uv + u^{2} }{2a}$

2as = $2uv - 2u^{2} + v^{2} - 2vu - u^{2}$

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

2as = $v^{2} - u^{2}$; or;  

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

∴ Proved