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OBJECTIVES:
You will learn to calculate the average and instantaneous velocity of
an object from a knowledge of its position at any time.
STEPS TO FOLLOW:
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Using Data Sheet I below, calculate the average velocity of
the ball between 1 and 4 seconds.
| t (sec)
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y (feet)
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| 0 |
6 |
| 1 |
90 |
| 2 |
142 |
| 3 |
162 |
| 4 |
150 |
| 5 |
106 |
| 6 |
30 |
Data Sheet I
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Connect the two points on the graph representing the ball's location at 1 and 4 seconds. Calculate the slope of this line and compare it to the ball's average velocity.
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Calculate the ball's average velocity over the shorter time intervals given on Data Sheet II below.
| t (sec)
|
y (feet)
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| 0 |
6.0 |
| 0.9 |
83.040 |
| 0.99 |
89.318 |
| 0.999 |
89.932 |
| 1.0 |
90.0 |
| 1.001 |
90.068 |
| 1.01 |
90.678 |
| 1.1 |
96.640 |
| 2.0 |
142.0 |
Data Sheet II
Fill In The Rate Of Change
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MATERIALS:
Calculator
Ruler
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Determine if the values you calculate over shorter and shorter time intervals are closing in on a limiting value. What is that value?
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Draw a line on your graph through the point (1, 90) with a slope equal to the value you found in the last question. This line should look approximately tangent to the graph. That is, it just touches the graph at the one point (1, 90).
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Pick another point on the graph, draw a tangent line, approximate its slope to determine the instantaneous velocity at that point.
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Find the point on the graph which has a horizontal tangent. What is happening to the ball at this time? What is its velocity?
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