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

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

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.

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 .

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

1. Collect Data

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 = . Changing curve = changing velocity ( ). Time Position Constant Velocity Position Time Changing Velocity

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

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

What information does the slope of the curve provide? sloped curve = movement in the 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 B is moving at the as C, but their starting is different. D is moving than B or C. Time Position A C B D

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

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. Since m = : v = 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 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.