Question

The velocity function (in meters per second) is given for a particle moving along a line. Your answer should be given in exact form, simplified as much as possible.

v(t)= 3t - 8, 0 ≤ t ≤ 5

(a) Find the displacement.
________m
(b) Find the distance traveled by the particle during the
given time interval.
________m

Answer 1

Explanation:

displacement is integral from t = 0 to 5 of vdt or (3t - 8) dt which you can work out.

distance is the integral from 0 to 5 of |v| dt. Easiest way to do this is to break up the integral into + and - parts and make the integrals positive. The zero for v is at 8/3 s, so

distance is the integral from t = 0 to 8/3 of -(3t-8)dt + integral from 8/3 to 5 of (3t -8)dt

Enjoy!