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physicsernaw
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Homework Statement
Given the following formula for distance, find the average velocity on the interval [1,3]
S(t) = t/(1+t^2)
Homework Equations
Vavg = (S(t0) - S(t1)) / (t0 - t1)
or
Vavg = (V0 + V1)/2
The Attempt at a Solution
I get two different answers and I need help understand why.
Vavg = (S(1) - S(3)) / (1-3)
Vavg = (1/2 - 3/10) / -2
Vavg = -2/20 = -1/10
Now using a different method, getting the instantaneous velocity at t = 1 and t = 3 by taking derivative of S(t) -> S'(t) = (1-t^2)/(1+t^2)^2
Vavg = (S'(1) + S'(3))/2
Vavg = (-8/100)/2 = (-2/25)/2 = -1/25
Why am I getting different averages here?? I don't understand what I'm doing wrong.
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