Graphing Motion Physics 11

Some humour to start…..

Cartesian Coordinates  Often use the Cartesian plane in order to identify an object’s position when describing motion  Same as the x-y plane used math class

Uniform Motion:  Predicting the behaviour of moving objects can be very complex. Measuring and analyzing motion in the real world is a challenge, so scientists try to simplify their task.  Scientists often try to model the behaviour of objects that move in almost straight lines at almost constant speed as uniform motion because this can be easily analyzed.  U niform motion : motion at constant velocity, with no change in speed or direction.

General rules to follow when graphing… 1. Independent variable goes on the x-axis 2. Dependent variable goes on the y-axis 3. Always label your axis so you know what they represent 4. Add a title to your graph 5. Draw a line of best fit if necessary

Lines of Best Fit  Best fit means to have an equal number of points above and below the line and equidistant from the line  This represents the average of the plotted points

Position-time graphs:  shows the position of an object over time  X-axis = time  Y-axis = position  The slope of a position- time graph is the velocity!!!!!

Position-Time Graphs Displacement in Meters Time in Seconds Displacement (m) Vs. Time (sec.) DisplacementTime

Position-Time Graph Displacement in Meters Time in Seconds Displacement (m) Vs. Time (sec.) Rise Run Slope = d f –d i t f - t i Or

Position-Time Graph Displacement in Meters Time in Seconds Displacement (m) Vs. Time (sec.) The Slope of this Line Remains Constant Throughout the Graph The constant slope indicates that the velocity of the object remains constant

Position-Time Graph Displacement in Meters Time in Seconds The velocity of this object changes over time….. Displacement (m) Vs. Time (sec.) B C A In which section is the object moving the fastest?

For position-time graphs showing uniform motion, then…  There are only three possible shapes for the graphs to take: 1. No motion, object is stationary d 3. Uniform motion to the left (backward) td 2. Uniform motion to the right (forward) d t

Let’s graph:  At the Berlin Marathon in 2008, Ethiopian Haile Gebrselassie set a new world record for the marathon with a time of 2:03:59. The key to Gebrselassie’s success is his ability to maintain a constant pace through out the event. His split times for each 5km interval (and half marathon and marathon splits) are given below. d(km)t(s)

1. Using the data table, plot his position (d) on the y-axis and his time (t) on the x-axis. Ensure that you choose a scale that will enable you to use as much of the graph paper as possible. 2. Using the data, draw a line of best fit to the data and determine the slope of the line. 3. What are the units for the slope in this instance? 4. For each 5km split (you can ignore the 21.1km and 42.2km) calculate his average speed (velocity) in m/s by dividing the distance in metres by the time in seconds. 5. Compare the results for your slope calculation to your results from question 4. What do you notice? What you can say about his pacing?

Some more practise:  WS