Describing MotionDescribing Motion

Physics 11Physics 11

Cartesian CoordinatesCartesian Coordinates

When we describe When we describe motion, we commonly motion, we commonly use the Cartesian use the Cartesian plane in order to plane in order to identify an object’s identify an object’s positionposition

This is simply the x-y This is simply the x-y plane that you are plane that you are familiar with from familiar with from math class math class

Cartesian CoordinatesCartesian Coordinates

When considering an object in Cartesian When considering an object in Cartesian Coordinates, it is important to determine a Coordinates, it is important to determine a reference (zero) pointreference (zero) point

This is often where the object starts but This is often where the object starts but can be an point that is convenientcan be an point that is convenient

Regardless of the reference point, all Regardless of the reference point, all calculations will give the same resultcalculations will give the same result

GebrselassieGebrselassie

At the Berlin Marathon in At the Berlin Marathon in 2008, Ethiopian Haile 2008, Ethiopian Haile Gebrselassie set a new Gebrselassie set a new world record for the world record for the marathon with a time of marathon with a time of 2:03:59. The key to 2:03:59. The key to Gebrselassie’s success is Gebrselassie’s success is his ability to maintain a his ability to maintain a constant pace through constant pace through out the event. His split out the event. His split times for each 5km times for each 5km interval (and half interval (and half marathon and marathon marathon and marathon splits) are given below.splits) are given below.

d(km) t(s)

0 0

5 875

10 1753

15 2643

20 3530

21.1 3725

25 4421

30 5307

35 6185

40 7054

42.2 7439

1.1. Using the data table, plot his position (d) on Using the data table, plot his position (d) on the y-axis and his time (t) on the x-axis. the y-axis and his time (t) on the x-axis. Ensure that you choose a scale that will enable Ensure that you choose a scale that will enable you to use as much of the graph paper as you to use as much of the graph paper as possible.possible.

2.2. Using the data, draw a line of best fit to the Using the data, draw a line of best fit to the data and determine the slope of the line. What data and determine the slope of the line. What are the units for the slope in this instance?are the units for the slope in this instance?

3.3. For each 5km split (you can ignore the 21.1km For each 5km split (you can ignore the 21.1km and 42.2km) calculate his average speed in and 42.2km) calculate his average speed in m/s by dividing the distance in metres by the m/s by dividing the distance in metres by the time in seconds.time in seconds.

4.4. Compare the results for each segment in part Compare the results for each segment in part 3 with the result for part 2. What do you 3 with the result for part 2. What do you notice? What you can say about his pacing? notice? What you can say about his pacing?

Vectors and ScalarsVectors and Scalars

ScalarsScalars– Most measurements Most measurements

you have used to this you have used to this point are scalarspoint are scalars

– This means that they This means that they have a magnitude have a magnitude (size)(size)

– They include They include measurements such measurements such as mass, energy, as mass, energy, distance, speed and distance, speed and timetime

VectorsVectors– Many measurements Many measurements

in Physics are vectorsin Physics are vectors– In addition to a In addition to a

magnitude they also magnitude they also have a directionhave a direction

– Velocity, Velocity, displacement, displacement, momentum and momentum and acceleration are all acceleration are all vector quantitiesvector quantities

Position VectorsPosition Vectors

A position vector is simply a vector (arrow) A position vector is simply a vector (arrow) that connects the reference point of a that connects the reference point of a coordinate system to an objectcoordinate system to an object

Reference PointPosition Vector

DisplacementDisplacement

Displacement is a vector quantity that Displacement is a vector quantity that measures the change in an object’s initial measures the change in an object’s initial and final positionand final position

12 ddd

Time and Time IntervalsTime and Time Intervals

In physics, we will In physics, we will often start timing often start timing when something when something occurs (this provides occurs (this provides a zero in time)a zero in time)

We may also consider We may also consider a time interval which a time interval which is symbolized as is symbolized as ΔΔtt

VelocityVelocity

Velocity is a vector quantity that is the rate Velocity is a vector quantity that is the rate of change of position; it is calculated as:of change of position; it is calculated as:

t

dv

If we remove the directional information If we remove the directional information from the velocity, we are left with speed:from the velocity, we are left with speed:

t

dv

• Position and time data can be analyzed using multiple representations: • motion diagrams• Vectors• Graphs• Equations

• Motion diagrams are a series of ‘dots’, numbered in succession and positioned to indicate direction

• Time interval between each dot is equal • As an object’s speed increases, the dots on its motion

diagram increase in separation• As an object’s speed decreases, the dots decrease in

separation

Examples of motion diagrams:

Situation: A skateboarder rolling down the sidewalk at constant speed.A constant distance between the positions of the moving skateboarder shows that the object is moving with constant speed.

Examples of motion diagrams:

Situation: A car stopping for a stop sign. A decreasing distance between the positions of the moving car shows that the object is slowing down.

Examples of motion diagrams:

Situation: A sprinter starting a race. An increasing distance between the positions of the moving runner shows that the object is speeding up.

Examples of motion diagrams:

Situation: A free throw in a basketball game. A more complicated motion (projectile motion) shows both slowing down (as the ball rises) and speeding up (as the ball falls).

• Motion diagrams develop operational definitions for different motions, i.e. constant speed, slowing down, speeding up

• Operational definitions are those defined in terms of particular procedure or operation performed by an observer.

• Assume for now that motion is translational along a path or trajectory

• An object is considered a particle, a mass at a single point in space

• Particles have no shape, size or distinction between front and back or top and bottom

Practice ProblemsPractice Problems

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