A particle moves along a horizontal path its velocity functi

A particle moves along a horizontal path; its velocity function v(t) is graphed below and the areas of each region (12, 16 and 10) are shown. Find the following. integral^5_0 v(t)dt integral^5_3 3v(t)dt Determine the object\'s displacement and the total distance it travels on the interval [0, 5].

Solution

(a) Sum of all segments = 12 + 16 + 10 = 38

(b) 3 X (Sum of segments starting from 3 to 5) = 3 * 10 = 30

(c) Distance = Displacement (As particle moves along horizontal path and do not change direction) :

Sum of area of all segment = distance travelled by particle = velocity * time(dt) = 12 + 16 + 10 = 38