1. Uniform Motion and Instantaneous Velocity
2.2 and 2.3 Review
Uniform Motion and
Instantaneous Velocity

2. Perform a 4 step analysis of section 2 of this graph
Position, m
Time (sec) 2 1

3. Perform a 4 step analysis of section 2 of this graph1 2

4. Calculate the displacement of the object whose motion is represented by this graph
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5. Which object has the largest displacement?

6. QuickCheck 2.11
Here is the velocity graph of an object that is at the origin (x  0 m) at t  0 s.
At t  4.0 s, the object’s position is
20 m
16 m
12 m
8 m
4 m
Answer: C
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7. QuickCheck 2.11
Here is the velocity graph of an object that is at the origin (x  0 m) at t  0 s.
At t  4.0 s, the object’s position is
20 m
16 m
12 m
8 m
4 m
Displacement  area under the curve
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8. Graphing Accelerated Motion Position vs Time Graphs
What kind of motion does each graph show?

9. Instantaneous Velocity
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10. Finding the Instantaneous Velocity
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11. In this magnified segment of the position graph, the curve isn’t apparent. It appears to be a line segment. We can find the slope by calculating the rise over the run, just as before:
vx = (1.6 m)/(0.20 s) = 8.0 m/s
This is the slope at t = 0.75 s and thus the velocity at this instant of time.
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12. Finding the Instantaneous Velocity
Graphically, the slope of the curve at a point is the same as the slope of a straight line drawn tangent to the curve at that point. Calculating rise over run for the tangent line, we get
vx = (8.0 m)/(1.0 s) = 8.0 m/s
This is the same value we obtained from the closeup view. The slope of the tangent line is the instantaneous velocity at that instant of time.
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13. Even when the speed varies we can still use the velocity-versus-time graph to determine displacement.
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