A particle has velocity v=3-t m,s-1 for 0

Question

A particle has velocity v=3-t m,s-1 for 0 <= t 5 seconds and initial displacement -1 m. Sketch its displacement–time and distance–time graphs, labelling endpoint and turning values. Mark its time at the origin and its rest time, and find its total distance.

Accepted Answer

Origin at $t=3-\sqrt7$ s; rest at $3$ s. Position values at $0,3,5$ s are $-1,\dfrac{7}{2},\dfrac{3}{2}$ m; distances are $0,\dfrac{9}{2},\dfrac{13}{2}$ m. Total distance $\dfrac{13}{2}$ m.

Origin crossing and a distance sketch

Origin crossing and a distance sketch

Solution:

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