Estimating Rate of Change of Velocity

We were introduced to a super fast car in the beginning of this module and now have the tools to calculate its acceleration at various times as it speeds up in a race.

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 to 100 mph in 5.88 seconds, from 0 to 200 mph in 14.51 seconds, and from 0 to 229.9 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.

First observe that 60 mph = 88 ft/s, 100 mph $\approx 146.67$ ft/s, 200 mph $\approx 293.33$ ft/s, and 229.9 mph $\approx 337.19$ ft/s. We can summarize the information in a table.

Now compute the average acceleration of the car in feet per second on intervals of the form $[t,19.96]$ as $t$ approaches 19.96, by creating a table for average acceleration. Does the rate at which the car is accelerating appear to be increasing, decreasing, or constant?

The rate at which the car is accelerating is decreasing as its velocity approaches 229.9 mph (337.19 ft/s).