Chapter 3 | Derivatives
225
Example 3.8 Chapter Opener: Estimating Rate of Change of Velocity
Figure 3.10 (credit: modification of work by Codex41, Flickr)
Reaching a top speed of 270.49 mph, the Hennessey Venom GT is one of the fastest cars in the world. In tests it went from 0 to 60 mph in 3.05 seconds, from 0 to100 mph in 5.88 seconds, from 0 to200 mph in 14.51 seconds, and from 0 to229.9 mph in 19.96 seconds. Use this data to draw a conclusion about the rate of change of velocity (that is, its acceleration) as it approaches 229.9 mph. Does the rate at which the car is accelerating appear to be increasing, decreasing, or constant? Solution First observe that 60 mph = 88 ft/s, 100 mph ≈146.67 ft/s, 200 mph ≈293.33 ft/s, and 229.9 mph ≈337.19 ft/s. We can summarize the information in a table. t v ( t )
0
0
3.05
88
5.88
147.67
14.51 293.33
19.96 337.19
Table 3.2 v ( t ) at different values of t
Now compute the average acceleration of the car in feet per second per second on intervals of the form ⎡ ⎣ t , 19.96
⎤ ⎦
as t approaches 19.96, as shown in the following table.
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