The equation of motion is given by s=sin2πt (m) . Find the acceleration after 4.5 sec

  1. 1. The equation of motion is given by s=sin2πt (m) . Find the acceleration after 4.5 seconds



    3. The attempt at a solution

    Im getting confused on whether the above equation is for velocity or distance.
    I know the derivative of distance is velocity and that the derivative of velocity is acceleration.
    If i take the derivative of the above equation i end up with
    Sa=cos 2π

    This eliminates T , So im not sure what im doing wrong.

    Thanks in advance for help.
    Cheers
     
  2. jcsd
  3. Dick

    Dick 25,887
    Science Advisor
    Homework Helper

    Re: The equation of motion is given by s=sin2πt (m) . Find the acceleration after 4.5

    Yes, s is distance. But the derivative d/dt sin(2*pi*t) definitely isn't cos(2*pi). Use the chain rule. What's the derivative of sin(t)? Does the t disappear?
     
  4. Re: The equation of motion is given by s=sin2πt (m) . Find the acceleration after 4.5

    Ok would i be correct in saying the derivative of
    S=sin2πt is Sv=2π cos 2πt ?
     
  5. Dick

    Dick 25,887
    Science Advisor
    Homework Helper

    Re: The equation of motion is given by s=sin2πt (m) . Find the acceleration after 4.5

    Yes, you would.
     
  6. Re: The equation of motion is given by s=sin2πt (m) . Find the acceleration after 4.5

    So to get the derivative of Sv=2π cos 2πt to find acceleration . Would i just use the chain rule again?

    If so does this look correct ?
    Sa=2π^2 sin 2πt?

    thanks
     
  7. Dick

    Dick 25,887
    Science Advisor
    Homework Helper

    Re: The equation of motion is given by s=sin2πt (m) . Find the acceleration after 4.5

    Sure, use the chain rule again. But try to do it right. The derivative of cos(t) isn't sin(t), it's -sin(t). And the number in front of the sin(2*pi*t) isn't 2pi^2. Take another try.
     
  8. Re: The equation of motion is given by s=sin2πt (m) . Find the acceleration after 4.5

    ok i still cant seem to get the correct answer. with this equation Sv=2π cos 2πt
    Im taking "2π cos " to be the outer function & 2πt to be the inner function

    so the derivative of "2π cos" would be just "-sin"
    And the derivative of "2πt" would be "2π"

    When i put it together i end up with is "-sin 2πt * 2π" or " Sa=-2π sin 2πt

    Can you please let me know where im going wrong. Thanks
     
  9. Ray Vickson

    Ray Vickson 6,315
    Science Advisor
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    Re: The equation of motion is given by s=sin2πt (m) . Find the acceleration after 4.5

    (d/dt)[2*pi*cos(2*pi*t)] = (2*pi)*(d/dt) cos(2*pi*t). You really do have to be more careful!

    RGV
     
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