position and time, derivative.

• Sep 20th 2009, 01:00 PM
mybrohshi5
position and time, derivative.
A particle moves along a straight line and its position at time http://webwork.asu.edu/webwork2_file...5b59f2bc11.png is given by http://webwork.asu.edu/webwork2_file...fc90ba4e71.png where http://webwork.asu.edu/webwork2_file...03d1ff8031.png is measured in feet and http://webwork.asu.edu/webwork2_file...5b59f2bc11.png in seconds.

1. Use interval notation to indicate when the particle is moving in the positive direction.
-----i thought this was [0,infinity) because it is always increasing?
but its wrong.

2. Find the total distance traveled during the first 8 seconds.
-----i thought i just plugged in 8 into the original equation but thats wrong too.

could i get some help on these two parts please =)

thank you

• Sep 20th 2009, 01:05 PM
skeeter
Quote:

Originally Posted by mybrohshi5
A particle moves along a straight line and its position at time http://webwork.asu.edu/webwork2_file...5b59f2bc11.png is given by http://webwork.asu.edu/webwork2_file...fc90ba4e71.png where http://webwork.asu.edu/webwork2_file...03d1ff8031.png is measured in feet and http://webwork.asu.edu/webwork2_file...5b59f2bc11.png in seconds.

1. Use interval notation to indicate when the particle is moving in the positive direction.
-----i thought this was [0,infinity) because it is always increasing?
but its wrong.

particle is moving in the (+) direction when v(t) > 0

2. Find the total distance traveled during the first 8 seconds.
-----i thought i just plugged in 8 into the original equation but thats wrong too.

total distance $\displaystyle \textcolor{red}{= \int_0^8 |v(t)| \, dt}$

...
• Sep 20th 2009, 01:12 PM
mybrohshi5
ok so if its >0 wouldnt the interval notation be (0,infinity)?

i just plugged that into my online math homework and it said that was wrong too?

and for the second part wouldnt it be 4064?
that was wrong too?

what am i doing wrong with these two?

thank you
• Sep 20th 2009, 01:29 PM
skeeter
Quote:

Originally Posted by mybrohshi5
ok so if its >0 wouldnt the interval notation be (0,infinity)?

i just plugged that into my online math homework and it said that was wrong too?

and for the second part wouldnt it be 4064?
that was wrong too?

what am i doing wrong with these two?

thank you

$\displaystyle s(t) = t^4 - 4t + 21$

$\displaystyle v(t) = s'(t) = 4t^3 - 4$

$\displaystyle 4t^3 - 4 = 0$ at $\displaystyle t = 1$

for $\displaystyle 0 \le t < 1$ , $\displaystyle v(t) < 0$ ... the particle is moving in the negative direction.

for $\displaystyle t > 1$ , $\displaystyle v(t) > 0$ ... the particle is moving in the positive direction.

$\displaystyle |s(1) - s(0)|$ = distance particle moves between $\displaystyle t = 0$ and $\displaystyle t = 1$

$\displaystyle |s(8) - s(1)|$ = distance particle moves between $\displaystyle t = 1$ and $\displaystyle t = 8$

your knowledge of the basics of rectilinear motion is lacking, particularly the difference between displacement and distance traveled ... recommend that you research the topic.