12. Prove that v' = u? + 2as.

Prove that v² = u² + 2as .

From first equation of motion,

v = u + at

=> at = v - u

=> t = v - u / a

From the second equation of motion, we have

s = ut + 1/2at²

Putting the value of t in above equation , we get:

s = u ( v - u /a ) + 1/2 a ( v - u/a )²

s = uv - u² / a + a( v² + u² - 2uv / 2a²)

s = uv - u² / a + v² + u² - 2uv / 2a

s = 2uv - 2u² + v² + u² - 2uv / 2a

2as = v² - u²

Explanation:

Let us assume a body moving with an initial velocity ' u '. Let it's final velocity be 'v' after a time 't' and the distance travelled by the body be 's'. We already have ,

⇒first equation of motion ( i )

⇒second equation of motion ( ii )

Putting the value of t from ( i ) in the equation ( ii )

{ v = u + at

or , at = v - u

or, t = v-u / a }

⇒ forth equation of motion

Hope I helped!

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t.                 w               e                 n                   t                 y                 c             h               a           r           a               c                 t             e             r             s        

the answer is b ) square root of 5