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Velocity/acceleration/position probs in Calc AB

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Der Läufer's picture
Joined: Feb 2007
Velocity/acceleration/position probs in Calc AB

I am hoping someone can help me out with a problem. I've talked to my teacher about, oh seven times or so, and I still don't understand how to do the particle/acceleration problems.
My current problem states: A particle moves along the x-axis so that its velocity at any time t is greater than or equal to 0 is given by v(t)=1-sin(2pit).
a) Find the acceleration---This I can do, as it's only the second derivative.
b) Find the values of t, 0 less than or equal to t less than or equal to 2, for which the particle is at rest.---I think I know the answer, but only from graphing the velocity equation on my calculator. I'm not sure how to do this using calc, enough to get credit on the AP exam. Any help would be wonderful.
c) Find the position x(t) of the particle at any time t if x(0)=0. I know I have to take the anti-derivative of the velocity, taking account C, then set it equal to 0 (I think that's right, anyway). I'm just not sure how to do that. If anyone can walk me though this, I would be eternally thankful.

Thanks! My brain seems to have died when it comes to calc...


mary008's picture
Joined: Nov 2007

for b, set the velocity fcn = to 0 and solve.
for c, you need to integrate the two parts *separately* and use u-substitution on the 2nd part.

check out my calc site:

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