Distance/displacement integration problem

1. Sep 27, 2012

zachem62

1. The problem statement, all variables and given/known data

Suppose that v(t)=t2 -2t -8, 1≤t≤6 is the velocity function (in meters per second) of a particle moving along a line. Find a) the displacement and b) the distance traveled by the particle during the given time interval.

2. Relevant equations

3. The attempt at a solution

so i integrated the velocity function at the interval 1 to 6 and got the answer (-10/3)m. so i have no idea if this is the distance or displacement and if it is one of those, then how would i find the other one?

thanks!
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

2. Sep 28, 2012

Ray Vickson

Think about whether the particle can change its direction of travel between times 0 and 6, and if it can, think about what the integral ∫v(t): t=0..6 actually computes.

RGV

3. Sep 28, 2012

zachem62

in the question it says that t can only be between 1 and 6 so i can't use any 0. and it is possible that the particle can change direction and my guess is this means that the integral ∫v(t): t=1 to 6 computes the distance. am i right?

then how would i get displacement? can u give me a hint? i know that its the final position minus initial position but i don't know if i'm supposed to get it by integrating the function or do something else.

4. Sep 28, 2012

ehild

5. Sep 28, 2012

HallsofIvy

Staff Emeritus
v(t)=t^2 -2t -8, 1≤t≤6
When t= 6, v(6)= 36- 12- 8= 16.
When t= 1, v(1)= 1- 2- 8= -11.
Now, what was the displacement? (Do you know what "displacement" means?)