A particle moves in a straight line with position relative to some origin \( \mathrm{O} \) given...

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A particle moves in a straight line with position relative to some origin \( \mathrm{O} \) given \( \mathrm{b} s(t)=t^{3}-3 t+1 \mathrm{~cm} \), where \( t \) is the time in \( \operatorname{seconds}(t \geq 0) \)
(a) Find the position of the particle when changes in direction occur.
(b) For what time intervals is the particles speed increasing?
(c) What is the total distance travelled for \( t \in[0,2] \) ?
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