Question

write detailed answer? Derive the formula for the kinetic energy of an object of mass m, moving with the velocity v​

Answer 1

Let the work done on the object causes a change in its velocity from u to V and let a be the acceleration. we know that the kinetic energy of a body moving with a certain velocity is equal to work done on the object to acquire that velocity from rest.

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Answer 2

Answer:

The formula for kinetic energy is: KE=1/2 mv² , where m is the object's mass and v is its velocity.

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Explanation:

We know F=ma also

a=F/m -(equation 1)

(F=force, m=mass, a=acceleration)

3rd equations of motion

v²-u²=2as

v² = 2as (our initial velocity was 0)

v²=2×F/m ×s(replacing a by eq.1 result)

v² =2Fs/m

v² m=2Fs

v²m/s=2F

mv²/2s = F-( equation 2)

W=Fs

W=mv²/2s×s(replacing F by result obtained in equation 2)

W=mv^²/2

W=1/2mv²

Hence, Formula for Kinetic energy is 1/2 mv².

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