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( (\pi t)/(4) )`

The velocity as function of time is

`v(t)= - (\pi)/(4) sin( (\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)