Expert: Paul Klarreich - 2/13/2011

Question
find the particles displacement for the given time interval. If
s(0)= 3, what is the particles final position?

v(t)= 40-9.8t , 0_< t _< 10
im not sure how to even start!

Answer
Questioner: gabby
Country: United States
Category: Calculus
Private: Yes  <<<< Fixed.  No private questions, please.
Subject: calculus...area between 2 curves
Question: find the particles displacement for the given time interval. If
s(0)= 3, what is the particles final position?

v(t)= 40-9.8t , 0_< t _< 10
im not sure how to even start!

.................................
You start by integrating  v(t), getting:

s(t) = 40t - 4.9t^2 + a constant, which you call s0.

Then you substitute  t = 0:

s(0) = 40(0) - 4.9(0)^2 + s0 = 3,
because you said s(0) = 3.

Then you solve for s0 and:

You can finish up now.