Expert: Paul Klarreich - 1/25/2010

Question
So this problem I'm working on says that the velocity of a function is v(t)=-t^2+4t-3 for a particle moving along a line. Find the displacement and the distance traveled by the particle during the time interval [0,5].

For the displacement I've looked at a few examples and the part I get stuck at is how you go from;

s(5)-s(0)= {5         {5
          |v(t)dt =  |-t^2+4t-3 dt = ???
          }0         }0

and then in the examples for instance the problem
v(t)=t^2-t-6 on interval [1,4]it goes to
= [(t^3/3)-(t^2/2)-6t]{4
                     |
                     }1
=-9/2

I'm not sure how you are getting the t^3 and t^2 and etc divided by a number.. What do you do to get that?? It is probably an easy answer it is just a lot of examples I have seen don't explain. Thanks.


Answer
Questioner: Brooke
Country: United States
Category: Calculus
Private: No
Subject: velocity problem
Question: So this problem I'm working on says that the velocity of a function is v(t)=-t^2+4t-3 for a particle moving along a line. Find the displacement and the distance traveled by the particle during the time interval [0,5].

For the displacement I've looked at a few examples and the part I get stuck at is how you go from;

s(5)-s(0)=
{5         {5
|v(t)dt =  |-t^2+4t-3 dt =  >> yes, that is so, but you need parentheses:
}0         }0


{5
|(-t^2+4t-3) dt =
}0


and then in the examples for instance the problem
v(t)=t^2-t-6 on interval [1,4]it goes to
= [(t^3/3)-(t^2/2)-6t] (from 1 to 4)

= -9/2

I'm not sure how you are getting the t^3 and t^2 and etc divided by a number..

What do you do to get that?? It is probably an easy answer it is just a lot of examples I have seen don't explain. Thanks.

........................
It IS an easy answer.  It is called the x^n rule for integration.  
Have you studied integrals yet?

I think you have, but I don't really understand what your question is.