# position function help!

• Mar 31st 2010, 06:24 PM
olemiss13
position function help!
A particle moves according to the position function
f(t)=sin(pi(t)/4) , t>or equal to 0 , t in seconds, s in feet.

a. find the average velocity of the particle over the interval [1,5]
b. when is the particle at rest in the first 10 seconds?
c. Find the total distance traveled during the first 10 seconds by drawing a path of the motion.

Thank you!!
• Mar 31st 2010, 06:31 PM
Jhevon
Quote:

Originally Posted by olemiss13
A particle moves according to the position function
f(t)=sin(pi(t)/4) , t>or equal to 0 , t in seconds, s in feet.

a. find the average velocity of the particle over the interval [1,5]
b. when is the particle at rest in the first 10 seconds?
c. Find the total distance traveled during the first 10 seconds by drawing a path of the motion.

Thank you!!

First note that the velocity function is given by $\displaystyle v(t) = f'(t)$

For (a): Average velocity on [1,5] = $\displaystyle \frac {f(5) - f(1)}{5 - 1}$

For (b): You want $\displaystyle v(t) = 0$, and solve for the $\displaystyle t$ values between 0 and 10

For (c): Distance traveled in the first 10 seconds = $\displaystyle \int_0^{10} |v(t)|~dt$