the velocity function (in meters per second) is given for a particle moving along a line.

Question

v(t) = 3t − 8,    0 ≤ t ≤ 3

(a) Find the displacement.

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

Answer 1

v = 3t -8 = s'

s= the integral of v = (3/2)t^2 - 8t + c

from t = 0 to 3

s(3) - s(0) = (3/2)(9) -12 - 0 = 27/2 -12 = 1.5 meters in 3 seconds