Question

derivation of 3rd equation of motion ​

Answer 1

Hi there,

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derv... of v²=u²+2as

v= final velocity

u=initial velocity

a=acceleration

s=displacement

so... basic.... we know .... v = ds/dt     (obviously)

speed = disp/tim

and  a = dv/dt

acceleration = (change in) velocity/unit time

=> a = dv/dt x ds/ds

and bcause ds/dt = v

we get

a=v dv/ds

=>

v dv = a ds

now (integration)

$\int\limits^v_u {v} \, dv=a\int\limits^s_0{} \, ds$

(v²-u²)/2 = as

=> v²=u²+2as

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Cheers

:)