Vault Of Euclid

Distance Traveled with a Negative Velocity

The definite integral warmup

Find the distance traveled by an object moving along a line with velocity \( v = (2-t)/\sqrt{t} \) from \( t=4 \) to \( t=9 \).
definite-integraldistance-traveledrectilinear-motionabsolute-valuepower-rulefundamental-theorem-of-calculusvelocityintegrationalgebraic-simplificationevaluating-integralskinematicscalculus-i

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What this problem tests

Tests the ability to recognize when a velocity function is negative and to correctly set up and evaluate the integral of its absolute value.

This is a standard application of the definite integral in a first-semester calculus course, introducing the distinction between displacement and total distance.

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