- #1

GustX

- 10

- 0

## Homework Statement

At time t, the position of a body moving along the s-axis is

[itex] s= t^3 -12t^2 + 36t m(meters)

[/itex]

Find the total distance traveled by the body from t = 0 to t = 3.

## Homework Equations

Derivatives

## The Attempt at a Solution

I got the derivative which is

3t^2 - 24t + 36(meters)

I set it equal to zero and got

t = sqrt[-4]

which wouldn't work out

I've also tried inputting the derivative into the quadratic formula and got

[itex]t = 4

[/itex]

[itex]

t = 2[/itex]

idk if that was neccesaryi tried inputting all the t values from interval 0-3 and got the following results

[itex]

0 -> 0

[/itex]

[itex]

1 -> 25

[/itex]

[itex]

2 -> 32

[/itex]

[itex]

3 -> 27

[/itex]

Trying to mimic the book I took the differences between each interval result

[itex]

(0 and 25) -> 25

[/itex]

[itex]

(25 and 32) -> 7

[/itex]

[itex]

(32 and 27) -> 5

[/itex]

[itex]

25 + 7 + 5 = 37

[/itex]

but that isn't the answer on the sheet either which is 59m

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