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Problem 31 Medium Difficulty

What speed must a particle attain before its kinetic energy is double the value predicted by the non relativistic expression $K E=\frac{1}{2} m v^{2} ?$

Answer

Velocity of the particle $=0.786151 \mathrm{c}$

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Video Transcript

Connecticut er's is equal to Oh, kinetic energy is equal to gum times m c square minus m c square And we have non relativistic kinetic energy Ah, non relativistic kinetic energy No. One, uh, ladder Mystic, uh, Connecticut or sheet is equal to huh m we square. This is the non relativistic kinetic energy. And according to the given question, we have gonna times m c square minus m C square is equal to em, we swear. And the skin before the return is m c square into one divided by, uh, square root off one minus we square divided by C square minus m c square. Since the latticed ick factor recalls one divided by square root of one minus, we squared, divided basically square on DDE is equal to em. We square and solving for we, uh, solving for weed we get We is equal to zero point 78 61516151 times the speed of light. So we lost two of the particle is super 20.786 151 times the speed off

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