A particle has accumulated distance D=2t m for 0

Question

A particle has accumulated distance D=2t m for 0 <= t 2, D=4 m for 2 <= t 3, and D=4+(t-3)2 m for 3 <= t 5, where time is in seconds. Sketch its speed–time graph and two different compatible velocity–time graphs. Explain why direction cannot be recovered uniquely from the distance graph.

Accepted Answer

Speed is $2$ on $(0,2)$, zero on $(2,3)$, then $2(t-3)$ on $(3,5)$, in $\mathrm{m\,s^{-1}}$. Two possibilities are velocity equal to this speed and velocity equal to its negative. Direction is not uniquely determined. At $2$ s the idealised graph has no two-sided slope.

What a distance graph cannot determine

What a distance graph cannot determine

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