How Do You Derive the Acceleration Function from a Given Velocity Equation?

[david98999]

Homework Statement

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.
[/B]
I am sure the process to get to the answer is a simple one but for some reason I am unable to see it

Homework Equations

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

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 generalI 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

 

[SteamKing]

Homework Statement

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.
[/B]
I am sure the process to get to the answer is a simple one but for some reason I am unable to see it

Homework Equations

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

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 generalI 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

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.

 

[david98999]

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.

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

 

[Orodruin]

the question wants me to derive the velocity as a function of time

So M and P are constants ... You should only differentiate with respect to time.

 

[david98999]

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