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QuestionPhysics

Using only dimensional analysis, convert 65 miles per hour to kilometers per second. Show your work and explain how you arrived at your answer.
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Answer

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Step 1:
I'll solve this problem using dimensional analysis, following the specified LaTeX formatting guidelines:

Step 2:
: List the given conversion factors

- 1 mile = $$1.60934~\mathrm{kilometers}
- 1 hour = 3600~\mathrm{seconds}

Step 3:
: Set up the dimensional analysis conversion

65~\frac{\mathrm{miles}}{\mathrm{hour}} \times \frac{1.60934~\mathrm{kilometers}}{1~\mathrm{mile}} \times \frac{1~\mathrm{hour}}{3600~\mathrm{seconds}}

Step 4:
: Cancel out units and multiply

65 \times \frac{1.60934}{3600}~\frac{\mathrm{kilometers}}{\mathrm{seconds}}

Step 5:
: Calculate the final value

= 0.0290~\frac{\mathrm{kilometers}}{\mathrm{seconds}}

Final Answer

Key Insight: Dimensional analysis allows direct conversion between units by systematically canceling and converting units through multiplication.