Average vs. Instantaneous Velocity

The graphs below show a ball thrown straight up (v₀ = 20 m/s). Drag the two dots on the position graph — or use the sliders — to set an interval [t₁, t₂]. The amber line has the same slope as the average velocity between those two points — it's drawn extended a bit past them so you can directly compare its angle to the violet tangent line at t₁, whose slope is the instantaneous velocity. Shrink Δt to zero and watch the amber line rotate onto the violet one — on both graphs at once.

x(t) and v(t) — the actual motion average slope & average velocity tangent & instantaneous velocity

t₁ / t₂

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Δt

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Δx

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v_avg = Δx / Δt

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v_inst = dx/dt at t₁

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|v_avg − v_inst|

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Start time, t₁ –

Interval width, Δt –