total dist. of s(t) = 4t^3 - 15t^2 + 18t - 3 from t = 0 to 2

[math]

A position function is given by s(t) = 4t^3 - 15t^2 + 18t - 3.

Find total distance traveled from t = 0 to t = 2.

s'(t) = v(t) = 12t^2 - 30t + 18 = 0 t=1 t=3/2

I'm confused regarding how to find the total distance, because the velocity is equal to 0 at more than one place (for example, at t=1). I think I would do the following:

abs (s(2) - s(1)) + abs(s(1) - s(0))

But what should I do about the velocity being zero at 1 s and 3/2 s?

Thank you!

 

[tkhunny]

You need an arc length.

\(\displaystyle \sqrt{1\;+\;(f'(t))^{2}}\)

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