Finding velocity function from a model of forceby Falken_47 Tags: acceleration, differential, velocity 

#1
Feb912, 09:12 PM

P: 9

1. The problem statement, all variables and given/known data
Hi, I've got an assignment which involves finding the function of velocity against time, given the information that the particle is moving with intial velocity of v_{0} and that it experience a resistive force of βv^{2} 2. Relevant equations From the problem I've derived model of: ma = βv^{2} 3. The attempt at a solution rearranging the model, I have equation of: dv/dt = β/m * v^{2} then, using techniques from seperable equation, dv/v^{2} = β/m * dt 1/v = β/m * t + C_{1} pluging in v(0) = v_{0} 1/v_{0} = β/m * 0 + C_{1} Or C_{1} = 1/v_{0} Now, plugging in C and rearraging the equation, I obtained 1/v = β/m * t  1/v_{0} v = m/(β * t) + v_{0} So as you can see, I'm able to derived the velocity function, but the problem lies to the fact that if I try to plug in t=0 for the velocity, then the function will not work as division by zero is not allowed Therefore, I'm thinking that something is wrong with my velocity function but up till now I can't still figure it out Thank you in advance! 



#2
Feb912, 09:40 PM

Emeritus
Sci Advisor
PF Gold
P: 5,198

Welcome to PF!
Your calculus is fine, you just forgot how to do division:[tex]\frac{1}{v(t)} = \frac{\beta}{m} t + \frac{1}{v_0}[/tex][tex]\Rightarrow v(t) = \left[ \frac{\beta}{m} t +\frac{1}{v_0} \right]^{1} \neq \frac{m}{\beta t} + v_0 [/tex] 



#3
Feb1012, 12:36 AM

P: 9

Ah yes thank you very much at pointing out my mistake, guess I spend too much time thinking how to actually solve the differential equation that I forgot about that. In any case, thank you for helping me again :)



Register to reply 
Related Discussions  
Finding position from velocity (trig function)  Introductory Physics Homework  7  
Finding velocity from gforce?  General Physics  2  
Finding recoil velocity only given force and firing velocity  Introductory Physics Homework  3  
Finding the Velocity from Acceleration as a function of position  Calculus & Beyond Homework  8  
Force as a Function of Velocity (Lorentz Force)  Introductory Physics Homework  4 