Motion in One Dimension (Position vs. Time) Chapter 5.1

1. Motion in One Dimension (Position vs. Time)Chapter 5.1

2. Distance, Position and Displacement • Distance: The distance that an object has moved irrespective of your starting position. • Ex. You walk 3 meters north and then walk 3 meters south. What distance have you traveled? • meters

3. Distance, Position and Displacement • Position: Where you are relative to a or point. • Ex.: You walk meters north. • Your position is meters from your starting or reference point.

4. Distance, Position and Displacement • Displacement: A measure in distance relative to a point that includes . • Ex.: You walk 3 meters north and then 3 meters south. What is your displacement? • meters. • Ex.: Your walk 3 meters north and 4 meters east. What is your distance traveled? What is your displacement? • Distance: meters. • Displacement: meters .

5. Motion of Objects • To describe the motion of an object, what other information will we need other than position, distance or displacement? • If I have the object’s and , what can be determined about the object’s motion? • or • Now, lets look at some data

6. 1. Collect Data

7. 2. Choose appropriate axes and plot the data.

8. 3. Draw a curve that provides a “best fit” to the points.

9. Position Position Position Position Time Time Changing Velocity Constant Velocity What information does the shape of the curve provide? • Straight line = . • Changing curve = changing velocity ().

10. Position Position Time Position Position Time Position Position Position Position Time Time What information does the shape of the curve provide? Negative Positive Decreasing Increasing

11. E D C Position B A Position Time Characterize the motion of the object from A to E. in the positive direction. . . . in the positive direction.

12. Position Position Position Position Time Time Negative Direction Positive Direction What information does the slope of the curve provide? • sloped curve = movement in the direction. • sloped curve = movement in the direction.

13. C Position B Position A D Time What else does the slope tell us? • What is the motion described by each curve? • How does the velocity of each curve compare to one another? • A is • B is moving at the • as C, but their starting • is different. • D is moving than • B or C.

14. Analyzing motion of more than one object. • Two vehicles travel through a speed trap traveling at two different velocities.

15. y = 11.65x - 13.07 R = 1.00 2 y = 1.13x + 4.08x - 0.05 2 R = 1.00 2 Determining the slope of the curve. 1997 World Championships - Athens, Greece Maurice Green 100 90 80 70 60 Distance (m) 50 40 30 20 10 0 0 2 4 6 8 10 Time (s)

16. 1997 World Championships - Athens, Greece Maurice Green Slope = 100 90 m = 80 y = 11.65x - 13.07 m = 70 2 R = 1.00 Distance (m) 60 50 40 30 4 5 6 7 8 9 10 Time (s) Velocity determined from the slope of the curve. m = Since m = : v = m/s

17. Key Ideas • Although space exists in 3 dimensions, analysis of objects in motion can be limited to one dimension to simplify problems. • When graphing position vs. time, use the x-axis for and the y-axis for . • By analyzing the shape of a position vs. time graph, the relative motion of the object can be determined, i.e. constant velocity, acceleration, stationary. • The slope of the position vs. time graph provides the over the time interval.