Answer:
[tex](a)v(t)=-\frac{\pi }{3}sin(\frac{\pi t}{3})[/tex]
(b)-0.91 ft/s
Step-by-step explanation:
Given the position function s = f(t) where f(t) = cos(πt/3), 0 ≤ t ≤ 6
(a)The velocity at time t in ft/s is the derivative of the position vector.
[tex]If\: f(t)=cos(\frac{\pi t}{3})\\f'(t)=-\frac{\pi }{3}sin(\frac{\pi t}{3})\\v(t)=-\frac{\pi }{3}sin(\frac{\pi t}{3})[/tex]
(b)Velocity after 2 seconds
When t=2
[tex]v(2)=-\frac{\pi }{3}sin(\frac{\pi *2}{3})\\=-0.91 ft/s[/tex]
The particle moves 0.91 ft/s in the opposite direction.
