How many joules of energy are required to accelerate a 1.0-kg mass from rest to a speed of 86.6% the speed of light? (c = 3.00 × 10⁸ m/s) A) 1.8 × 10¹⁷ J B) 9.0 × 10¹⁶J C) 2.7 × 10¹² J D) 4.5 × 10⁹ J E) 3.0 × 10³ J

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Quizplus · Accepted Answer

The relativistic kinetic energy is calculated using the formula $ KE = (\gamma - 1)mc^2 $, where $\gamma = \frac{1}{\sqrt{1 - v^2/c^2}} $. For $ v = 0.866c $, $\gamma = 2$. Thus, $ KE = (2 - 1)(1 \, \text{kg})(3.00 \times 10^8 \, \text{m/s})^2 = 9.0 \times 10^{16} \, \text{J} $.

How Many Joules of Energy Are Required to Accelerate a 1.0-Kg