The change in kinetic energy is twice the change in momentum
Explanation:
The momentum of an object is given by:
[tex]p=mv[/tex]
where
m is the mass of the object
v is its velocity
While the kinetic energy is given by
[tex]K=\frac{1}{2}mv^2[/tex]
We want to check how these two quantities change when the speed of the object doubles, therefore when the new velocity is
[tex]v'=2v[/tex]
For the momentum, we have
[tex]p'=mv'=m(2v)=2(mv)=2p[/tex]
So, the momentum doubles.
For the kinetic energy, we have
[tex]K'=\frac{1}{2}mv'^2=\frac{1}{2}m(2v)^2=4(\frac{1}{2}mv^2)=4K[/tex]
So, the kinetic energy quadruples.
Therefore, the change in kinetic energy is twice the change in momentum.
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