Rest and return on a cubic journey
Rest and return on a cubic journey
7 marks
TGM Original
A particle moves on a straight line with displacement s=t3-6t2+9t metres for 0 <= t 4 seconds. Find its velocity and acceleration. State its rest times, the times it is at the origin, and its intervals of motion in each direction.
Solution:
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Answer:\(v=3t^2-12t+9\ \mathrm{m\,s^{-1}},\ a=6t-12\ \mathrm{m\,s^{-2}}\). Rest at \(t=1,3\) s; origin at \(t=0,3\) s. Positive direction for \(0\le t<1\) and \(3<t\le4\); negative for \(1<t<3\).
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