21. If an object’s speed is doubled, how does its Kinetic Energy change?

Monday, December 8, 2008

21. If an object’s speed is doubled, how does its Kinetic Energy change?

Hello!

For an object with a mass $\displaystyle{m}$ and a speed $\displaystyle{V}$ its kinetic energy is defined as

$\displaystyle{E}_{{k}}={m}\frac{{{V}}^{{2}}}{{2}}.$

So if a speed is doubled, $\displaystyle{V}_{{1}}={2}{V},$ and a mass remains unchanged, then

$\displaystyle{\left({E}_{{k}}\right)}_{{1}}={m}\frac{{{\left({V}_{{1}}\right)}}^{{2}}}{{2}}={m}\frac{{{\left({2}{V}\right)}}^{{2}}}{{2}}={4}\cdot{\left({m}\frac{{{V}}^{{2}}}{{2}}\right)}={4}{E}_{{k}}.$

Thus the kinetic energy will be quadrupled (4 times greater than the original).

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Monday, December 8, 2008

21. If an object’s speed is doubled, how does its Kinetic Energy change?

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