MCAT Physics Question 70: Answer and Explanation
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Question: 70
10. An electron is accelerated over a distance d by an electrical potential V. The electrical potential applied to this electron is then increased by a factor of 4 and the electron is accelerated over the same distance d. The speed of the electron at the end of the second trial will be larger than at the end of the first trial by a factor of:
- A. 16
- B. 8
- C. 4
- D. 2
Correct Answer: D
Explanation:
The electrical potential (V) is equal to the amount of work done (W) divided by the test charge (q). This means that the potential is directly proportional to the amount of work done, which is equal to the amount of energy gained by the particle; therefore, the overall amount of energy increases by a factor of 4. Because energy is directly proportional to the square of the speed (according to 
), the speed must increase by a factor of 2.