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1. Use a position vs. time graph to interpret an object’s position or displacement.
2. Define velocity.
3. Differentiate between speed and velocity.
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Slope is the rate of change for the object.
How far it moves in y for every x.
Slope = rise/run = change of y / change of x
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Displacement (d) or Position (p) on the y-axis
Time (t) on the x-axis
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What it is not…
A picture of the path taken by the person or object.
Going up?
Actual path was flat.
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What can a p-t graph tell you?
Instantaneous Position: Position at a particular instant (an instant lasts zero seconds).
Starting point: The y-intercept tells you the object’s starting point. If an object starts at the measuring device, then its’ y-intercept is 0. If it starts 3 meters away, then its y-intercept is 3 m.
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Intersection of 2 lines tells you when 2 objects have the same position.
What can a p-t graph tell you?
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Don’t be a dope…What about slope?
∆y
∆x
1. Pick two points on your line.
2. Subtract the y points.
3. Subtract the x points.
4. Divide the rise by the run.
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Slope of a p-t graph = Average Velocity
∆y
∆x=
∆d
∆t
v = =df - di
tf - ti
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Now, let’s look at units…
∆y
∆x=
∆d
∆t
The SI base unit for displacement is meters.
The SI base unit for time is seconds.
Therefore, units are m/s.
In other words, slope tells how many meters the object (runner) moved in 1 second.
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The absolute value of the slope of a p-t graph tells you the average speed (how fast the object is moving).
Velocity is a vector = Magnitude & Direction
Speed is a scalar = Magnitude
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Instantaneous Velocity = the speed and direction of an object at a particular instant.
Can be found by finding the tangent to a point on a position-time graph.