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# A particle is moving with the given data. Find the position of the particle.$a(t) = t^2 - 4t + 6$, $\quad s(0) = 0$, $\quad s(1) = 20$

## $$s(t)=\frac{1}{12} t^{4}-\frac{2}{3} t^{3}+3 t^{2}+\frac{211}{12} t$$

Derivatives

Differentiation

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##### Catherine R.

Missouri State University

##### Heather Z.

Oregon State University

##### Kristen K.

University of Michigan - Ann Arbor

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### Video Transcript

we know that velocity is the integral or anti derivative of acceleration. Therefore, let's check the integral when we got 1/3 t cute. Remember, the exponent goes up by one and then we divide by the new explain it when we're taking in the rolls. Now that we've got that, we know that position is the integral velocity. Now, remember, as a 00 and we end up with B our constant equal zero now remember us of one is 1 12 comes one to the fourth, minus 2/3 times one cubed plus three times one squared, plus eight times one, which is said able to 20 therefore are constant A is 211 over 12. Therefore, a final equation as 50 is 1 12 t to the fourth, minus 2/3 T cubed murders three T squared plus 211 over 12 t

#### Topics

Derivatives

Differentiation

Volume

##### Catherine R.

Missouri State University

##### Heather Z.

Oregon State University

##### Kristen K.

University of Michigan - Ann Arbor

Lectures

Join Bootcamp