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The speedboat in Figure 2.11 has a constant acceleration of +2.0 m/s2. If the initial velocity of the boat is +6.0 m/s, find its displacement after 8.0 seconds.
| | Figure 2.11
(a) An accelerating speedboat. (b) The boat’s displacement x can be determined if the boat’s acceleration, initial velocity, and time of travel are known. (© Onne van der Wal/Corbis Images) |
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Reasoning
Numerical values for the three known variables are listed in the data table below. We wish to determine the displacement x of the speedboat, so it is an unknown variable. Therefore, we have placed a question mark in the displacement column of the data table.
Speedboat Data
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x
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a
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v
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v0
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t
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?
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+2.0 m/s2
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+6.0 m/s
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8.0 s
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We can use  to find the displacement of the boat if a value for the final velocity v can be found. To find the final velocity, it is necessary to use the value given for the acceleration, because it tells us how the velocity changes, according to v =v0+at.
Solution
The final velocity is
 | (2.4) | |
The displacement of the boat can now be obtained:
 | (2.7) | |
A calculator would give the answer as 112 m, but this number must be rounded to 110 m, since the data are accurate to only two significant figures.
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