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Question

# When a particle doubles its speed from $0.45 c$ to $0.90 c$, the relativistic energy will increase by more than a factor of four.

Solution

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Step 1
1 of 2

This statement is true as the connection between the speed and energy is not quadratic but

$K=\left(\frac{1}{\sqrt{1-v^2/c^2}}-1\right)m_0c^2$

So we have that

$\frac{E_1}{E_2}=\frac{\frac{1}{\sqrt{1-0.9^2}}-1}{\frac{1}{\sqrt{1-0.45^2}}-1}=10.8\gt4$

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