Practice question · Multiple choice
The definite integral of a velocity that goes negative gives displacement, not distance travelled. Why does the integral come out smaller than the odometer?
Hints
- Drive 10 km out and 10 km back. What does the odometer say, and where are you?
- Ask what the signed area under a negative velocity represents.
Show the answer
D. Because area below the axis counts as negative and cancels
Why
The signed area cancels: out and back gives zero displacement and twenty kilometres on the odometer. Integrating |v| recovers the distance, which is why the sign convention is not a nuisance but the thing that makes the integral answer 'where did it end up' rather than 'how far did it go'.
Practise The Definite Integral
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