QQuestionPhysics
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.
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