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Using acceleration data to find velocity

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An object is dropped straight down from a helicopter. The object falls faster and faster but its acceleration (rate of change of its velocity) decreases over time because of air resistance. The acceleration is measured in ft/sec^2 and recorded every second after the drop for 7 seconds, as shown below.

t a
0 32.00
1 19.41
2 11.77
3 7.14
4 4.33
5 2.63
6 1.59
7 0.97

Find an upper estimate for the distance fallen when t = 3.

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Solution Summary

How do we use physical data to find an "upper limit" for velocity? We explore this question in the following solution.

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Break the problem down into 3 time intervals, 0-1s, 1-2s, and 2-3s.

From 0-1s, the speed will be 32 ft/s, so the object falls 32 feet.

From 1-2s, the speed increases by 19.41 ft/s to become 51.41 ft/s, so the object ...

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