8. Displacement and distance from velocity Consider the velocity function shown

Question

8. Displacement and distance from velocity Consider the velocity function shown below of an object moving along a line. Assume time is measured in seconds and distance is measured in meters. The areas of four regions bounded by the velocity curve and the r-axis are also given. a. On what intervals is the object moving in the negative direction? b. What is the displacement of the object over the interval [2, 61? c. What is the total distance traveled by the object over the interval [0, 6]? d. What is the displacement of the object over the interval [0, 81? e. Describe the position of the object relative to its initial position after 8 hours.

Explanation / Answer

a) Moving in negative direction when velocity is negative

Hence in (0,2)U(4,6)

b) displacement in (2,6) = integral of velocity curve = Area bounded by vel curve

= 14+10 =24

c) Total distance travelled = Total area covered in (0,6) = 20+14+10 =44

d) In (0,8) distance travelled = (20+14+10+6) = 50

e) After 8 hours total distance trvelled =50

in that in positive direction - 20

Negative direction - 30

Net displacement = -10 (or 10 units in the negative direction)

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