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Velocity Drag force and distance traveled

  • Thread starter nysnacc
  • Start date
  • #1
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Homework Statement


Microsoft-Edge-Web-Notes-Mastering61302359[2305843009214067476].jpg


Homework Equations


Sum of force

a = dv/dt
v = integrate a + C

The Attempt at a Solution



I found the equation in terms of final v, initial v... however, on the right hand side, there is another v, and I think it is time dependent, so I am not sure which value should I plug in.
 

Answers and Replies

  • #2
TSny
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Try using the chain rule to write ##a = \frac{dv}{dt} = \frac{dv}{dx} \frac{dx}{dt}##.
 
  • #3
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Then do we know dv/dx and dx/dt? on the right hand side, will the velocity be initial one? thanks
 
  • #4
TSny
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Then do we know dv/dx and dx/dt?
Try to express F = ma as a differential equation in terms of just the variables v and x. dv/dx is already expressed in these variables. How can you express dx/dt?

on the right hand side, will the velocity be initial one? thanks
v on the right side of a = F/m is the instantaneous velocity.
 
  • #5
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so dv/dx * dx/dt = -40/m v^2 ??
 
  • #6
TSny
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so dv/dx * dx/dt = -40/m v^2 ??
Yes. In order to get only the variables v and x to appear in the equation, what can you do with dx/dt?
 

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