Question

Derive the expression Vsquare=usquare+2ax

Answer 1

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Newtons third equation of motion says that the square of final velocity of a body is equal to sum of square of its initial velocity and double of the product of its acceleration and displacement or distance.

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

Where :-

v = final velocity

u = initial velocity

a = acceleration

s = displacement

Derivation :-

Now we know that according to first equation of motion

$v = u + at$

Where :-

v = final velocity

u = initial velocity

a = acceleration

t = time taken

If we square this equation on both sides we get:

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

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

Now according to second equation of motion we know

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

Thus replacing part of equation by s we get :

$\star \: {v}^{2} = {u}^{2} + 2as$

Hence derived.

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BY SCIVIBHANSHU

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