A particle has velocity v=(t-2)2 m,s-1 for 0

Question

A particle has velocity v=(t-2)2 m,s-1 for 0 <= t 4 seconds. Sketch its speed–time and distance–time graphs, marking the rest time and endpoint values. Explain whether its distance graph has a maximum at rest.

Accepted Answer

Speed $(t-2)^2\ \mathrm{m\,s^{-1}}$; distance $D=\dfrac{t^3}{3}-2t^2+4t$ m. Rest at $2$ s; distances $0,\dfrac{8}{3},\dfrac{16}{3}$ m at $0,2,4$ s. No distance maximum occurs at rest.

Graphs at rest without a reversal

Graphs at rest without a reversal

Solution:

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