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Derive a Velocity function

  1. Jul 13, 2015 #1
    1. The problem statement, all variables and given/known data

    Derive the function for the acceleration from this function

    v=√(2P/M)(√T)

    The answer is √(P/2MT)

    I have tried many different attempts but I am still unable to reach this answer.

    I am sure the process to get to the answer is a simple one but for some reason I am unable to see it

    2. Relevant equations
    I use the normal method of deriving the function , for each variable i use anx^(n-1)

    3. The attempt at a solution

    We have 3 variables P , M and T

    derivative of P

    (1/2)P^(-1/2) =1/(2√P)

    derivative of M

    (-1/2)M^(-3/2)= -M^(-3/2)/2

    Derivative of T

    (1/2)T^(-1/2)= 1/(2√T)


    these answers do not make up the final sum as m is negative ,

    I just need to understand the process to get to the answer for this particular sum , not the subject in general


    I can derive and integrate functions (ex: 3x^2= 3(2)x^(2-1)=6x and 6x^2/2=3x^2)
    its just that I do not understand how to derive this equation into the given answer ,
    I have a mental block about this question.I would appreciate any help

     
  2. jcsd
  3. Jul 13, 2015 #2

    SteamKing

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    It's not clear what P and M stand for in the formula for velocity. Is T supposed to represent time?

    The acceleration has a very specific definition: it is the derivative of the velocity with respect to time. If P or M are not functions of time, then they are treated as constants when taking any derivatives w.r.t. time.
     
  4. Jul 13, 2015 #3
    sorry the function is to find the velocity of an alfa romero car , p= the power in watts , m is the mass and t is the time , the question wants me to derive the velocity as a function of time
     
  5. Jul 13, 2015 #4

    Orodruin

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    So M and P are constants ... You should only differentiate with respect to time.
     
  6. Jul 13, 2015 #5
    You are right I did as you said

    √(2p/m)*√t

    a=dv/dt=(2p/m)^(1/2) x t^1/2 = 2^(-1) x (2p/m) ^(1/2) x t^(-1/2)
    = √(2p/(m(2)^2)t)= √(p/2mt)

    I had a feeling it was a simple error , i'm sorry I wasted every ones' time.
    Thank you for your help
     
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