I have successfully completed all parts of the following problem, except the par

Question

I have successfully completed all parts of the following problem, except the part requiring that I determine the earliest times of maximum speed and maximum acceleration.

Problem: The displacement of an object is x = (8.0 cm)cos(2.0t + pi/3), where x is in centimeters and t is in seconds. Calculate (a) the speed and acceleration at t = pi/2 seconds, (b) the maximum speed and the earliest time (t>0) at which the particles has this speed, and the maximum acceleration and the earliest time (t>0) at which the particles has this acceleration.

Answers: a) 8(3^1/2) cm/s and 16 cm/s^2
b) 16 cm/s and t = ?????
c) 32 cm/s^2 and t = ?????

I understand that it's against the Cramster rules to post two questions in one. However, I believe finding the time for either part will be very similar to finding the time for the other. If you are not comfortable with answering two questions, then I ask that everyone only give information on how to determine the time in part B. Thanks!

Explanation / Answer

x = (8.0 cm)cos(2.0t + pi/3) v = dx/dt = -16sin(2t + pi/3) A = 8 , w=2 Vmax = Aw = 8*2 = 16 cm/s it occurs when 2t + pi/3 = pi/2 t = pi/12 seconds a = dv/dt = -32 cos(2t + pi/3) a max = 32 m/s^2 it occurs 2t+pi/3 = pi t = pi/3 s

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