6.1a The Net Change in Position, Displacement and Distance Traveled by a Moving Body Rita Korsunsky

. . . . If a body moving along the line reverses direction while it travels, for example: it moves 3m forward, then 4 m back, then 6 m forward, then its Net Change of the position is: 3-4+6=5m, and the Total Distance is: 3+4+6=13m . . . . 3 5 Displacement is defined to be the change in position of an object. It can be defined mathematically with the following equation:

Net Change in Position or Displacement If an object moves along the line and its velocity is a continuous function of time, then object’s position is: where F is antiderivative of v. Displacement of the object or Net Change in object’s Position during time t = a to t = b is link

Calculating Net Change in Position Yielding the general form: The velocity of a moving body along a line is Find the net change in the body’s position from time t=0 to time t=3/2 So, the net effect of the motion from t=0 to t= 3/2 is to shift the body 5 m to the left

Example

Example Time (sec) 4 6 9 10 Velocity (in/sec) 12 15 5

Total Distance traveled by the body If the body moves along the line 6m forward and then 6m backward, the net change of body’s position is 0, but the total distance is 12m. To calculate the total distance with the integral, we have to keep the contributions of the forward motion and a backward motion from canceling each other out. So integrate the absolute value of the velocity from a to b. a b c Total Distance Traveled Along a Line a b c

Total Distance Total Distance Traveled Along a Line The velocity of a body moving along a line is Find the total distance traveled by the body from t=0 to t=3/2 Total Distance =

Example