Question

Help with calculus question?? The motion of a particle is described by the equation s = 10cos(5t - pi/4) What are the max values of the displacement, the velocity, and the acceleration? At what times do these max occur? What are the min values of these quantities?

Answer 1

MaxDisp = Max (10 cos(5t- pi/4)) = 10*Max(cos[5t -pi/4])
cos(5t -pi/4) = 1 -> max of cos function
5t - pi/4 = 0
5t = pi/4
t = pi/20
s(pi/20) = 10*cos(pi/4 - pi/4) = 10* cos(0) = 10

Answer 2

the amplitude or max displacement is 10

find s' max velocity is at s = 0 find t when s = 0

acceleration find s" max acceleration is at s = 10 find t

Answer 3

Thank you guys so much, i was having trouble with what to do after differentiating them, but now i get it!