At time t in seconds, a particle’s distance s⁢(t), in centimeters, from a point is given by s⁢(t)=13sin⁢ t+40. What is the average velocity of the particle from t⁢= π3 to t⁢= 13π3?

Respuesta :

Answer:

Explanation:

Given

distance [tex]s(t)=13\sin (t)+40[/tex]

at [tex]t=\frac{\pi }{3}[/tex]

[tex]s(\frac{\pi }{3})=13\sin (\frac{\pi }{3})+40[/tex]

[tex]s(\frac{\pi }{3})=13\times \frac{\sqrt{3}}{2}+40[/tex]

at [tex]t=\frac{13\pi}{3}=4\pi+\frac{\pi}{3}[/tex]

[tex]s(4\pi+\frac{\pi}{3})=13\sin (4\pi+\frac{\pi}{3})+40[/tex]

Average velocity is change in position w.r.t time

[tex]v_{avg}=\frac{s(4\pi+\frac{\pi}{3})-s(\frac{\pi }{3})}{4\pi+\frac{\pi}{3}-\frac{\pi }{3}}[/tex]

[tex]v_{avg}=0[/tex]