Question

(h) when is the particle speeding up? (enter your answer using interval notation.) (2,4)∪(6,8) incorrect: your answer is incorrect. f(t) = cos(πt/4)

Answer 1

The position of the particle as function of time is given as
$f(t)=cos( \frac{\pi t}{4} )$

The velocity as function of time is
$v(t)= - \frac{\pi}{4} sin( \frac{\pi t}{4} )$

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)