# Kinematics - how do u find distance travelled

1. Jul 25, 2006

### meee

ok. so i have x(t) = something and v(t) = something

i know x will give me the displacement for a set time

say if i wanted the distance travelled in the first ten seconds, i know i can use the definite integral of velocity.

Is there any easier way? like using the displacement equation?

2. Jul 25, 2006

### 0rthodontist

Actually you can't use the definite integral of velocity-you have to use the definite integral of the absolute value of velocity or else you'd be measuring displacement and not distance. You don't want the distance travelled to start decreasing just because the velocity becomes negative.

Since it is in 1 dimension, if it never turns around, then its distance travelled after 10 seconds is the absolute value of its position after 10 seconds. If it does turn around and double back on its path then what can you say about the distance?

3. Jul 25, 2006

### meee

then it would be double!

lol ok... so if i have like a parabola graph of displacement/time i can just add up from the y values of start to max/mins and end point etc.

4. Jul 25, 2006

### Hootenanny

Staff Emeritus
As orthodontist said, you must use the integral of the modulus of your function of velocity;

$$\int^{10}_{0} \left| v(t) \right| dt$$

The process is quite laborious and not one of my favourite things to do, have you solved modulus functions before?
Yes, that would work (I think)

5. Jul 25, 2006

### meee

sweet thanks guys
yeah ive done modulus functions