At the moment t=0 a particle starts moving along thr x-axis so that its velocity projection varies as vx= 35 cos pi t cm/s, where 't' is expressed in seconds. Find the distance that this particle covers during t = 2.80 s after the start.

Answer 1

It will move back and forth along the x axis with frequency 0.5 Hz.

If distance covered is defined as
DeltaX = xfinal - xinitial, then

Delta X = Integral vx dt
0 to 2.8 s
= 35 pi sin(2.8 pi)

The particle will be in its second back-and-forth period, and will have "covered" 4 amplitudes during the first period.