Concept 6
Perform unit conversions and dimensional analysis; track units consistently.
Set up unit conversions so unwanted units cancel and the final unit matches the question.
Core Idea
Set up the calculation so unwanted units cancel. If the units do not cancel correctly, the setup is wrong even if the arithmetic is clean.
Understanding
Rule: Dimensional analysis is a structure check as much as a computation.
Write the rate with its full unit, multiply or divide so the unwanted unit cancels, and convert again if the question asks for a different final unit. This is one of the safest ways to catch a mistake before you finish, because the units tell you whether the operation makes sense.
Question
Worked Example
A runner moves at
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