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Interpreting Graphs
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Several important characteristics of graphs are listed in the right hand frame. Lets apply them to the Figure 1. What is the initial temperature? |
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By this we mean the temperature at the start of the data. Here that is 200 degrees. What happens to the temperature between 0 and 1 minute? |
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Nothing. The temperature is the same at 0 and 1 minute. Between what minutes is the temperature dropping the fastest? |
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Between 2 and 3 minutes. Between what minutes is the temperature rising the fastest? |
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Between 7 and 8 minutes. When is the temperature the lowest? |
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Between 4 and 6 minutes. At 3 minutes, is the temperature rising or falling? |
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Falling. Now consider Figure 2. This graph represents the height of a ball thrown from the top of a building. Time is measured starting when the ball is thrown. What is the height of the building? |
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Since the graph starts at a height of 110 feet at time = 0 seconds, the height of the building must be 110 feet. For how many seconds is the ball rising? |
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We see that the height increases for approximately the first 3 seconds. How long is the ball at a height of 255 feet? |
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Only a fraction of a second. How can you tell that? |
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The curve looks flat from 2.8 to 3.2 seconds. |
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The ball starts falling. How far does the ball fall between times of 4 and 5 seconds? |
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About 40 feet. How far does the ball fall between times of 5 and 6 seconds? |
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About 90 feet. What happens at time = 7 seconds? |
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The ball hits the ground. Another way of graphing this situation is shown in Figure 3. Notice that the shape of the curve is the same. What is different? |
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The ball starts at a height of 0 feet. What is the height at t = 7 seconds? |
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At t = 7 seconds, the height is about -110 feet. How can we have a negative height? |
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Notice that the origin is at the beginning of the graph, so that the initial height of the ball is 0 feet. This means that measurements of height are made from the top of the building. The negative height at time = 7 seconds represents the ball hitting the ground 110 feet below the starting point, which was the top of the building. Does the ball reach its highest point at the same time as before? |
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Yes, the maximum height is reached at time = 3 seconds, just as in Figure 2. |
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