Tangent to a position–time graph for instantaneous velocity

An example figure from the Motion Graph Generator.

A position–time graph curving upward for 6 s, with a dashed tangent line touching the curve at 4 s — A position–time graph of a cart speeding up steadily from rest for 6 s, so the line curves upward. A dashed tangent line touches the curve at 4 s; its slope is the cart’s instantaneous velocity at that moment.

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Answer key

A to B (0–6 s): speeding up from 0 to 6 m/s, a = 1 m/s²; 0 m to 18 m
Tangent at 4 s: it touches at 8 m, and its slope, the instantaneous velocity, is 4 m/s

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