The velocity function is v(t) = t^2 - 6 t + 8 for a particle moving along a line. Find the displacement and the distance traveled by the particle during the time interval [-1,5]. what is the displacement

Question

The velocity function is v(t) = t^2 - 6 t + 8 for a particle moving along a line. Find the displacement and the distance traveled by the particle during the time interval [-1,5].  what is the displacement

anonymous · Answer

Uh don't you have some sort of initial condition in the question? Otherwise when you integrate how are you going to solve for the constant?

anonymous · Answer

well actually question is all about this nothing more actually i tried to solve this question but my supervisor said that isnot correct this is the solution that i answer to him
-[-125/3 +75 - 40] - [-1/3 +3-8]

anonymous · Answer

it's the integral of your function from -1 to 5. 
there's no need for an initial condition because it's asking for the distance travled IN the time span. 

$$\int\limits_{-1}^{5} (t ^{2} - 6t + 8) dt$$

anonymous · Answer

lol oh yeah oops forgot

anonymous · Answer

I think the question is actually a little more subtle that that.

In this interval (unless I am imagining it wrong) the direction changes (twice!), so you need to conider this for the DISTANCE. The displacement is just your standard plug and chug integral.

anonymous · Answer

yeah it crosses the axis at 2 and 4 so you just calculate the integral from -1 to 2, the integral from 2 to 4 and and from 4 to 5 and add all their absolute values up together.