Vectors A runner ran 400 m around a track. What was her displacement? A runner ran 400 m around a track. What was her displacement? A. zeroB. 400 mC. 400

VectorsVectors

A runner ran 400 m around a track. What was A runner ran 400 m around a track. What was her displacement?her displacement?

A. zeroA. zero B. 400 mB. 400 m C. 400 m [around]C. 400 m [around]

A tiger paces 20 m [W] and 10 m [E]. What A tiger paces 20 m [W] and 10 m [E]. What was the tiger’s displacement?was the tiger’s displacement?

A. zeroA. zero B. 30 mB. 30 m C. 10 m [E]C. 10 m [E] D. 10 D. 10 m [W]m [W]

True or false?: The average velocity of an True or false?: The average velocity of an object can be zero even if the object is moving.object can be zero even if the object is moving.

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Graphing Displacement and Graphing Displacement and Velocity: Learning GoalVelocity: Learning Goal

The student will be able to create The student will be able to create and analyse displacement-time and analyse displacement-time graphs and velocity-time graphs of graphs and velocity-time graphs of motion in one dimension (using motion in one dimension (using slopes of displacement-time graphs slopes of displacement-time graphs to find velocities and using the area to find velocities and using the area under velocity-time graphs to find under velocity-time graphs to find displacement). (B2.2)displacement). (B2.2)

Graphing Graphing Displacement and Displacement and

VelocityVelocitySPH3USPH3U

Practice Question 1 Practice Question 1 ReduxRedux

Although Leah jogged at a constant Although Leah jogged at a constant speed for 1 minute, she spent the speed for 1 minute, she spent the first 30 s of that minute jogging first 30 s of that minute jogging North and the second 30 s jogging North and the second 30 s jogging South.South.


Her Her velocityvelocity, which is a vector , which is a vector quantity defined as the rate of quantity defined as the rate of change in her displacement, was change in her displacement, was therefore 3 m/s [North] (or 3 m/s if therefore 3 m/s [North] (or 3 m/s if we designate North the positive we designate North the positive direction) for the first 30 s and 3 m/s direction) for the first 30 s and 3 m/s [South] (or -3 m/s if we designate [South] (or -3 m/s if we designate South the negative direction) for the South the negative direction) for the second 30 s.second 30 s.

+

_


Plot Leah's Plot Leah's velocityvelocity on the grid below with on the grid below with time on the horizontal axis and velocity on time on the horizontal axis and velocity on the vertical axis. Label your axes! the vertical axis. Label your axes! (Note (Note that there is a discontinuity at 30 s.)that there is a discontinuity at 30 s.)





Area UnderArea Under

The area under a velocity-The area under a velocity-time graph will be equal time graph will be equal to the displacement. Use to the displacement. Use the graph to calculate the graph to calculate the displacement at 0 s, the displacement at 0 s, 10 s, 20 s, etc.10 s, 20 s, etc.

Note that an area under Note that an area under the horizontal axis will the horizontal axis will be a negative area.be a negative area.

Area UnderArea Under

Example: Example:

At 40 seconds, the area under the At 40 seconds, the area under the graph is:graph is:

Displacement-TimeDisplacement-Time

Plot the data points in the table with Plot the data points in the table with time on the horizontal axis and time on the horizontal axis and displacement on the vertical axis. Label displacement on the vertical axis. Label your axes!your axes!


Plot the data points in the table with Plot the data points in the table with time on the horizontal axis and time on the horizontal axis and displacement on the vertical axis. displacement on the vertical axis. Label your axes!Label your axes!


Where is Leah relative to her starting Where is Leah relative to her starting position at the end of the 1 minute?position at the end of the 1 minute?


Where is Leah relative to her starting Where is Leah relative to her starting position at the end of the 1 minute?position at the end of the 1 minute?

At her starting point.At her starting point.

Average VelocityAverage Velocity

We can find the average velocity over We can find the average velocity over any time interval by finding the any time interval by finding the slope of the line connecting the slope of the line connecting the endpoints of the interval on the endpoints of the interval on the displacement-time graph. displacement-time graph.

What was Leah’s average velocity over What was Leah’s average velocity over the 1 minute time interval?the 1 minute time interval?

Average VelocityAverage Velocity

We can find the average velocity over any We can find the average velocity over any time interval by finding the slope of the time interval by finding the slope of the line connecting the endpoints of the line connecting the endpoints of the interval on the displacement-time graph. interval on the displacement-time graph.

What was Leah’s average velocity over the What was Leah’s average velocity over the 1 minute time interval?1 minute time interval?

0 m/s because her displacement was 0 m/s because her displacement was zero.zero.

More Practice Interpreting More Practice Interpreting GraphsGraphs

The graph at right shows the The graph at right shows the position-time or displacement-time position-time or displacement-time graph of a radio controlled car.graph of a radio controlled car.(Positive = [forward])(Positive = [forward])On a separate sheet of graph paper,On a separate sheet of graph paper, Describe each segment of the motion in Describe each segment of the motion in

words.words. Sketch the corresponding distance-time Sketch the corresponding distance-time

graph.graph. Sketch the corresponding velocity-time Sketch the corresponding velocity-time

graph.graph.


Describe each segment of the motion in Describe each segment of the motion in words.words.

Between 0 and 2 s, the car is travelling atBetween 0 and 2 s, the car is travelling at



Between 0 and 2 s, the car is travelling at 4 Between 0 and 2 s, the car is travelling at 4 m/s [fwd].m/s [fwd].

Between 2 s and 4 s,Between 2 s and 4 s,



Between 0 and 2 s, the car is travelling at 4 Between 0 and 2 s, the car is travelling at 4 m/s [fwd].m/s [fwd].

Between 2 s and 4 s, the car is at rest.Between 2 s and 4 s, the car is at rest.



Describe each segment of the motion in words.Describe each segment of the motion in words.

Between 0 and 2 s, the car is travelling at 4 m/s Between 0 and 2 s, the car is travelling at 4 m/s [fwd].[fwd].


Between 4 s and 9 s, the car is travelling at 2 m/s Between 4 s and 9 s, the car is travelling at 2 m/s [back].[back].



Describe each segment of the motion in words.Describe each segment of the motion in words.

Between 0 and 2 s, the car is travelling at 4 m/s Between 0 and 2 s, the car is travelling at 4 m/s [fwd].[fwd].


Between 4 s and 9 s, the car is travelling at 2 m/s Between 4 s and 9 s, the car is travelling at 2 m/s [back].[back].



On a separate sheet of graph paper,On a separate sheet of graph paper, Sketch the corresponding distance-Sketch the corresponding distance-

time graph.time graph.


On a separate sheet of graph paper,On a separate sheet of graph paper, Sketch the corresponding distance-Sketch the corresponding distance-



On a separate sheet of graph paper,On a separate sheet of graph paper, Sketch the corresponding velocity-Sketch the corresponding velocity-



On a separate sheet of graph paper,On a separate sheet of graph paper, Sketch the corresponding velocity-Sketch the corresponding velocity-


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Vectors A runner ran 400 m around a track. What was her displacement? A runner ran 400 m around a track. What was her displacement? A. zeroB. 400 mC. 400