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Ocasta
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Homework Statement
An object moves with velocity v(t) = −t2 +1 feet per second between t = 0 and t = 2. Find the average velocity and the average speed of the object between t = 0 and t = 2
Homework Equations
[itex]
\frac{1}{b-a} \int_a^b f'(x) dx
[/itex]
avg value of a function
The Attempt at a Solution
[itex]
\frac{1}{2-0} \int_0^2 [-t^2 + 1] dt
[/itex]
[itex]
\frac{1}{2} [- \frac{t^3}{3} + t]_0^2
[/itex]
[itex]
\frac{1}{2} [- \frac{8}{3} + \frac{6}{3}]
[/itex]
[itex]
\frac{1}{2} [- \frac{2}{3}]
[/itex]
[itex]
[- \frac{1}{3}]
[/itex]
So I've got the average velocity down, but I don't see how they want me to come up with the average speed. I know that speed and velocity are similar, but speed has no direction.
The book (http://www.whitman.edu/mathematics/multivariable/" ) Instructed me to evaluate the integral without the averaging [itex]\frac{1}{b-a}[/itex], but I ended up with:
[itex]
- \frac{2}{3}
[/itex]
But according to the solutions manual, the answer is 1
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