# Distance and Displacement Question

• Feb 26th 2011, 05:19 PM
softballchick
Distance and Displacement Question
The velocity function is http://math.webwork.rochester.edu:80...111267d211.png for a particle moving along a line. Find the displacement and the distance traveled by the particle during the time interval [0,6].

displacement = distance traveled =

OK so I found the displacement which is -12, but I can't find the distance. I know I have to find when it changes directions and I found it did that at x=3. Can someone help? Thanks
• Feb 26th 2011, 05:33 PM
topsquark
Quote:

Originally Posted by softballchick
The velocity function is http://math.webwork.rochester.edu:80...111267d211.png for a particle moving along a line. Find the displacement and the distance traveled by the particle during the time interval [0,6].

displacement = distance traveled =

OK so I found the displacement which is -12, but I can't find the distance. I know I have to find when it changes directions and I found it did that at x=3. Can someone help? Thanks

Assuming that your v(t) is a velocity, then you have got it right:
$\displaystyle \vec{s(t)} = \int_0^6 v(t) dt$

To find a distance, which is the magnitude of the velocity:
$\displaystyle s(t) = \int_0^6 |v(t)| dt$

where |v(t)| is the magnitude of the velocity, in this case the absolute value of the velocity function. Here are the two relevant graphs.

-Dan