A particle moves along the x-axis so that its velocity at any time t ≥ 0 is given by

Question

𝑣(𝑡) = (2𝜋− 5)𝑡− sin(𝜋𝑡)
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].

Answer 1

A. no difficulty here.
a(t) = v'(t) = (2π-5) - πcos(πt)
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