Displacement and Velocity Problem

Question

Given a velocity function v(t)=3t-5 (in meters per second) for a particle in motion from time t=0 to time t=3 find the following: 1.The net displacement of the particle. 2. The total distance traveled by a particle according to the given velocity over the interval [0,3].

Answer 1

Jenna, I think you are missing some information in the problem, but perhaps not.

We know v(t) = 3t - 5 so displacement is s(t) = 3/2t² - 5t + C the missing information would allow us to find a value for "C" and then be able to find displacement and the total distance travelled.

If we want "net displacement," then we look at s(3) - s(0) (and we don't need to know the value of "C"-- can you see why?)

If we want total distance travelled, we find the value of the definite integral with bounds 0 to 3 and the integrand is absolute value of v(t) (and make sure you understand why we don't need to know the value of "C")

Is there something about where the object was at some point in time? Just checking to make sure you were not asked to find a specific position of the particle at a given time.

Hope this makes sense