Question:
The velocity of a particle at which the kinetic energy is equal to its rest energy is
The velocity of a particle at which the kinetic energy is equal to its rest energy is
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When kinetic energy equals rest energy, use relativistic formulas to find the speed of the particle.
Updated On: Jan 6, 2026
- \( \frac{3c}{2} \)
- \( \frac{c}{\sqrt{2}} \)
- \( \frac{3c}{2} \)
- \( \frac{c\sqrt{3}}{2} \)
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The Correct Option is D
Solution and Explanation
Step 1: Relating kinetic and rest energy.
At the velocity \( v \), the kinetic energy is equal to the rest energy. This gives us the relation \( \frac{1}{2}mv^2 = mc^2 \), leading to \( v = c \sqrt{3}/2 \).
Step 2: Conclusion.
Thus, the velocity at which the kinetic energy equals the rest energy is \( \frac{c\sqrt{3}}{2} \), so the correct answer is option (D).
Final Answer: \[ \boxed{\frac{c\sqrt{3}}{2}} \]
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