Kinematics - how do u find distance travelled

[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 traveled 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?

 

[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 traveled to start decreasing just because the velocity becomes negative.

Since it is in 1 dimension, if it never turns around, then its distance traveled 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?

 

[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.

 

[Hootenanny]

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?

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.

Yes, that would work (I think)

 

[meee]

sweet thanks guys
yeah I've done modulus functions