Moving backward cancels forward displacement, but it does not erase distance traveled.
WHAT HAPPENS IF…For a=1, b=2, t=3, what are displacement and distance?
Interactive exploration
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Connect the picture to the ideaΔs=∫0tv(τ)dτ,D=∫0t∣v(τ)∣dτ
Here v(t)=at−b with a>0,b≥0. The displacement is at²/2−bt. Velocity changes sign at b/a, so total distance is found by splitting the integral there and reversing the sign of the negative part. These are exact results for the chosen linear velocity.
A detail that matters
A negative net displacement does not mean negative distance.