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

Distance, Position and Displacement Distance: The total 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? 6 meters

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

Distance, Position and Displacement Displacement: A measure in distance relative to a starting point that includes direction. Ex.: You walk 3 meters north and then 3 meters south. What is your displacement? 0 meters. Ex.: Your walk 6 meters north and 8 meters east. What is your distance traveled? What is your displacement? Distance: 14 meters. Displacement: 10 meters NE.

Motion of Objects To describe the motion of an object, what other information will we need other than position, distance or displacement? Time If I have the object’s position and time, what can be determined about the object’s motion? Speed or Velocity, or Acceleration. Now, lets collect some data

1. Collect Data Collect bowling ball data and have students plot it on a graph.

2. Choose appropriate axes and plot the data.

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

What information does the shape of the curve provide? Straight line = constant velocity. Changing curve = changing velocity(i.e. acceleration). Time Position Constant Velocity Position Time Changing Velocity

What information does the shape of the curve provide? Positive Acceleration Negative Acceleration Time Position Time Position Decreasing Velocity Position Time Position Time Increasing Velocity

Characterize the motion of the object from A to E. Constant velocity in the positive direction. Decreasing velocity. Stationary. Increasing velocity. Time Position A B C D E

What information does the slope of the curve provide? Positively sloped curve = movement in the positive direction. Negatively sloped curve = movement in the negative direction. Time Position Positive Direction Time Position Negative Direction

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 stationary B is moving at the same speed as C, but their starting position is different. D is moving slower than B or C. Time Position A C B D

What is the significance of the slope of the position vs. time curve? Since position is on the y-axis and time is on the x-axis, it follows that the slope of the line would be: Therefore, slope must equal speed or velocity. Time Position

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

Velocity determined from the slope of the curve. rise run df – di tf – ti 85m-50m 8.4s-5.4s m = 11.7m/s Since m = v: v = 11.7 m/s 1997 World Championships - Athens, Greece Maurice Green y = 11.65x - 13.07 R 2 = 1.00 30 40 50 60 70 80 90 100 4 5 6 7 8 9 10 Time (s) Distance (m) Slope = m = m =

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 time and the y-axis for position. 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 average velocity over the time interval.

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

What can be inferred from the following graph?