Question

The velocity function, in feet per second, is given for a particle moving along a straight line. v(t) = 2 cos(t), 0 ≤ t ≤ 3 a) Find the displacement. (b) Find the total distance that the particle travels over the given interval.

Answer 1

measures the length of the path of a particle in motion. The displacement is the shortest path from the initial to the final position of the particle. Given the velocity function , the displacement on a time interval is computed by
. While the distance is the total length of the path taken by the particle. On the same time interval and velocity, the distance is calculated by .
.

Answer and Explanation:
(a)

The displacement is computed by getting definite integral of the velocity function over the given time interval.







Evaluate at the limits of the integral to get the displacement.