# Total Distance of a Velocity Function

## Homework Statement

An object moves along the x-axis starting off from the initial position x(0)=3.
What is the total distance traveled by the object over the time interval [0,3].

## Homework Equations

The integral of the function from 0 to a plus the absolute value of the integral of the function from a to 3, where F(a) = 0.

## The Attempt at a Solution

I've tried a number of attempts to factor out any zeroes and, finding none, I resorted to a TI-89, confirming the assumption(not good, seeing as this is an AP Cal AB no-calculator practice test, for a test which is tomorrow morning).

I don't know where I'm going wrong in my procedure, but I keep getting 3. The answer I know is 23/3, and the initial position shouldn't matter a bit since its a definite integral and will only be negated anyway. It should be a simple integral from 0 to 3 of the velocity function with respect to t, but I keep getting the wrong answer.

siddharth
Homework Helper
Gold Member

## Homework Statement

An object moves along the x-axis starting off from the initial position x(0)=3.
What is the total distance traveled by the object over the time interval [0,3].

## Homework Equations

The integral of the function from 0 to a plus the absolute value of the integral of the function from a to 3, where F(a) = 0.

Can you post the question exactly as it was given to you? Is the velocity of the particle as a function of time given in the question? What's F(a)?

Stupid of me to forget the function.
v(t) = 4-t^2

Office_Shredder
Staff Emeritus