Can I use integration to show why car 2 traveled farther than car 1 over a given time interval?(adsbygoogle = window.adsbygoogle || []).push({});

Here is some of the problem,

I have the following graph of two different velocity functions

for two cars.

http://img97.imageshack.us/img97/5696/graph1kv.jpg" [Broken]

The viewing window of this graph is x from 0 to 30

and y from 0 to 100.

After integrating the velocity function I found the position function.

Estimating the distances traveled by both cars from time t = 0

to time = 30 I find,

Car 1whose velocity function is thethin lineon the graph

traveled approximately964.11 feet.

Car 2whose velocity function is thethick lineon the graph

traveled approximately1977.9 feet.

By looking at the graph it is obvious that the thick line has

a larger region under the curve (from the curve to the x-axis) than

the thin line.

Is it possible to integrate from 0 to 30 on each velocity function and show that the larger regions under the curve correspond to a higher average velocity over time interval 0 to 30 which is why car 2 traveled farther? Am I on the right track about dealing with the velocities of the cars? Should I also consider their acceleration as being a reason for why car 2 traveled farther?

I need explain why car 2 traveled farther. Is it possible to use integration to find average velocity?

In the original problem velocity is given every 5 seconds from 0 to 30 for each car. I could find the secant line over each 5 second interval and average those secant lines to find the approximate average velocity from time 0 to 30, correct? If possible I want to try to use integration to solve this.

Thanks

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# Homework Help: Calc I - Finding average velocity using integration

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