John Q.

asked • 11/28/20

The velocity of a particle...

The velocity function is 𝑣(𝑡)=−𝑡^2+3𝑡−2.

v(t)=−t^2+3t−2 for a particle moving along a line. Find the displacement and the distance traveled by the particle during the time interval [−2,6].

displacement = ?

distance traveled = ?



Zach J.

tutor
First, factor as v(t) = -(t-2)(t-1) This tells us that v(t) can be viewed as a downward-pointing parabola, with zeros at t=1,2. That is, v(t) is positive on the interval (1,2), and negative elsewhere. Integrating v(t) on the interval [-2,6] gives the displacement. For the distance travelled, we want to keep track of all of the distance, whether travelling in the positive or negative direction. So, for distance integrate the absolute value of v(t).
Report

11/29/20

1 Expert Answer

By:

Still looking for help? Get the right answer, fast.

Ask a question for free

Get a free answer to a quick problem.
Most questions answered within 4 hours.

OR

Find an Online Tutor Now

Choose an expert and meet online. No packages or subscriptions, pay only for the time you need.