Question

A particle moves along the x-axis so that its velocity at any time t β‰₯ 0 is given by
𝑣(𝑑) = (2πœ‹βˆ’ 5)π‘‘βˆ’ sin(πœ‹π‘‘)
A. Find the acceleration at any time t.
B. Find the minimum acceleration of the particle over the interval [0, 3].
C. Find the maximum velocity of the particle over the interval [0, 2].
A. no difficulty here.
a(t) = v'(t) = (2Ο€-5) - Ο€cos(Ο€t)
B. Now find where a'(t) = 0 and a"(t) > 0
C. find where v'=0 and v" < 0

You can check your work by looking at the graph at

https://www.wolframalpha.com/input/?i=plot+%282%CF%80-5%29t+-+sin%28%CF%80t%29%2C+%282%CF%80-5%29+-+%CF%80*cos%28%CF%80t%29+for+0+%3C%3D+t+%3C%3D+3

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