x = ( 0.0521 m) cos(6.655 t + 0.09 ? ) v = ? ( 0.347 m/s) sin(6.655 t + 0.09 ? )

Question

x                                                                              =                                                                              (0.0521 m) cos(6.655t + 0.09?)                                                                                v                                                                              =                                      ?(0.347 m/s) sin(6.655t + 0.09?)                                                                                a                                                                              =                                      ?(2.307 m/s2) cos(6.655t + 0.09?)                                      Use the equations below. (Note that the direction is indicated by the sign in front of the equations.) Determine the first time (t > 0) that the position is at its maximum (positive) value. s Set the argument of the sine or cosine function to the value that satisfies the stated condition, and solve for the time. Determine the first time (t > 0) that the velocity is at its maximum (positive) value. s Set the argument of the sine or cosine function to the value that satisfies the stated condition, and solve for the time.

Explanation / Answer

Position is max ==> cos theta = 1
==> 6.655t + 0.09pi= 0,2pi etc
0 cannot be as theta >1
Hence 6.655t + 0.09pi = 2pi
==>t = .902 s
Similarly for velocity we have
6.655t + 0.09pi = 3pi/2
==>.666 sec

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