Question

If the speed of the object is doubled and what is the kinetic energy to it's momentum?

Answer 1

If the momentum of an object is doubled, but its mass does not increase (so velocity remains well below the speed of light), then its velocity is doubled. If the velocity is doubled then the kinetic energy increases by the square of 2, or four time. Hence kinetic energy of the body will be 4 times to its eirlier value.

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Answer 2

If the speed of the object is doubled, the ratio of the kinetic energy to its momentum is v:1.

Explanation:

The kinetic energy of an object is given by :

$K=\dfrac{1}{2}mv^2$

m is mass

v is the speed of the object

The momentum of an object is given by :

$p=m\times v$

If the speed of the object is doubled, new kinetic energy becomes :

$K'=\dfrac{1}{2}m(2v)^2=2mv^2$.........(1)

If the speed of the object is doubled, new momentum becomes :

$p'=m\times (2v)$......(2)

Dividing equation (1) and (2) we get :

$\dfrac{K'}{p'}=\dfrac{2mv^2}{2mv}=\dfrac{v}{1}$

If the speed of the object is doubled, the ratio of the kinetic energy to its momentum is v:1.

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Kinetic energy

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