2. Distance, Displacement, and Acceleration for Linear Motion Lesson 10-2

3. Distance vs. Displacement 5 steps Distance = 5 steps Displacement = 5 steps 2 steps Distance = 7 steps Displacement = 3 steps 5 steps Distance = 12 steps Displacement = –2 steps Displacement can be negative when you are on the other side of the starting point. Distance, however, is always non- negative.

4. Definitions Absolute value ensures distance is non-negative.

5. Example 1: A moving object has feet per second in the time interval [0, 3]. find the time subintervals in which the velocity is positive and in which it is negative. Outside domain t = 1 is a critical number Subintervals [0,1) negative (1,3] positive

6. Example 1: A moving object has feet per second in the time interval [0, 3]. find the time subintervals in which the velocity is positive and in which it is negative. t = 1 is a critical number Subintervals [0,1) negative (1,3] positive

7. Example 1: Find the displacement of the object over the interval. Find the distance of the object over the interval.

8. Example 2: An object has an acceleration given by (ft/sec/sec) on the interval. [0, 2π] with an initial velocity of –2. Find its displacement and distance on the interval. Since initial velocity is –2

9. Example 2: An object has an acceleration given by (ft/sec/sec) on the interval. [0, 2π] with an initial velocity of –2. Find its displacement and distance on the interval.

10. Example 3: An object travels along a straight line with with constant acceleration of 2 ft/sec 2. At, the object’s velocity is 11 ft/sec. How far does the object travel during the time interval when its velocity increases from 15 ft/sec to 21 ft/sec. therefore,

11. Example 3: An object travels along a straight line with with constant acceleration of 2 ft/sec 2. At, the object’s velocity is 11 ft/sec. How far does the object travel during the time interval when its velocity increases from 15 ft/sec to 21 ft/sec. Since we don’t know the time interval when the velocity increases we must find it so as to know the limits of integration.

12. If the car’s initial velocity was 20 mi/h approximately how far did the car go in this 24 second interval?

13. Average Acceleration = ½(1.3+1.7) Average Acceleration = ½(1.7+2.2)

17. Make sure to pay attention to your units