The position of the particle as function of time is given as
[tex]f(t)=cos( \frac{\pi t}{4} )[/tex]
The velocity as function of time is
[tex]v(t)= - \frac{\pi}{4} sin( \frac{\pi t}{4} )[/tex]
A graph of f(t) versus t and of v(t) versus t is shown below.
The velocity increases in the intervals t = (2, 6) and t = (10, 14) and with a periodicity of 8.
In the range t = [0, 16], the velocity increases in the interval t = (2,6)∪(10, 14).
Answer: (2,6)∪(10,14)
