Science, asked by singhrajindra3, 1 month ago

prove that KE=1÷2 mv^



Answers

Answered by kinzal
5

Proof :

 \sf \longrightarrow v² - u² = 2as \\

 \sf \longrightarrow s = \frac{v² - u²}{2a} \\

 \sf \longrightarrow The work done by the force is given by

 \sf \longrightarrow W = F. s

But,

 \sf \longrightarrow F = ma

So, we can write,

 \sf \longrightarrow W = ma. s

Now,

  •  \sf w = ma × \bigg( \frac{v² - u²}{2a} \bigg) \\

  •  \sf w = m × \cancel{a} × \bigg( \frac{v² - u²}{2 \: \: \cancel{a}} \bigg) \\

  •  \sf w = m \bigg( \frac{ v² - u²}{2} \bigg) \\

If body was initially at rest, then u = 0

  •  \sf w = m \bigg( \frac{v² - 0²}{2} \bigg) = \frac{mv²}{2} \\

 \sf \longrightarrow The work done is equal to the kinetic energy of the body. so, KE =  \sf \frac{mv²}{2} = \frac{1}{2} mv²

I hope it helps you ❤️✔️

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