Particle Dynamics Problem

  • Thread starter s4orce
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  • #1
s4orce
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1. A particle is moving along a straight line such that its acceleration is defined as a=(4s^2)m/s^2, where s is in meters. If v=-100m/s when s=10m and t=0, determine the particles velocity as a function of position.



2. V=ds/dt a=dv/dt



3. V=ds/dt a=dv/dt 1/dt=ads*vdv
Integral 100 to s 4s^2ds=Integral -100 to v vdv

Integral 4s^2=4s^3/3



What do I do now, the answer is 16.89 ft. but I don't know how-to get that from the derivation. Need Help Thanks!
 

Answers and Replies

  • #2
cristo
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What've you done here: 1/dt=ads*vdv?

Your first equation a=4s2 is a differential equation: namely [tex]\frac{d^2s}{dt^2}-4s^2=0[/tex]. Do you know how to solve such an equation?
 
  • #3
s4orce
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Integral 4s^2=4s^3/3
 
  • #4
s4orce
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help me solve this please
 
  • #5
s4orce
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need help i don't know what to do
 
  • #6
teknodude
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Cristo gave you the equation, so solve the diff eq. Also the answer to the problem that you posted 16.89 ft, is not right. The question isn't asking for a numerical answer.

Another way is take the equations you have V=ds/dt a=dv/dt and eliminate dt and just integrate and do the algebra.
 
  • #7
s4orce
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can you post how you did it please
 
  • #8
s4orce
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if you got 15, for the answer that's not it also
 
  • #9
cristo
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s4orce, the question is not looking for a numerical answer; it is looking for an expression for velocity. The way I would do it, would be to solve the ODE I gave you in post 2, and then differentiate the answer wrt time.

Do you know how to solve such a differential equation?

Please note that we will not do your homework for you here; it won't help you learn the subject! What we will be happy to do is to help guide you to answer, if you put some work in. Check this link for the PF rules on homework help: https://www.physicsforums.com/showthread.php?t=5374
 

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