1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Velocity, Acceleration and Distance

  1. Nov 1, 2007 #1
    1.11. If position of an object is given by: x(t) = A sin(ωt) where A is a constant and ω is
    the angular frequency.
    a) What is the instantaneous velocity at time t?
    b) What is the instantaneous acceleration at time t?
    c) Express the instantaneous velocity and the instantaneous acceleration in terms of
    x, ω and A.

    2. dx(t)/dt= v(t)

    3. a) For (a) I just took the derivative of the x function and got wAcos(wt)
    b) Same thing here but took the derivative for the answer i got in A and got
    c) This is where i had some trouble. I got the instantaneous acceleration part of the
    problem by substituting x for Asin(wt) and thus got a(t)=-w^2x. But i had no
    clue how to get v(t) in terms of x,w,A.

    What i did was set sin^2(wt) + cos^2(wt)=1 and solved for cos^2(wt). then plugged that into v^2(t)=w^2A^2cos^2(wt). I got v^2=w^2(A^2-x^2). After taking the square root i got v = +/-(w * sqrt(A^2-x^2). Is this right? should there be the +/- or is one ruled out?

    Thanks for the help in advance!\sqrt{}
    Last edited: Nov 1, 2007
  2. jcsd
  3. Nov 1, 2007 #2


    User Avatar
    Science Advisor
    Homework Helper

    Good job! No, you can't pick one of the +/-. You need them both. At a given value of x, v can be either negative or positive depending on whether x is increasing or decreasing. And it could be doing either.
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?