Constant Power and speed of particle relation

sAXIn

Hello all

I encounter a difficulty solving most simple problem related to constant power and speed of particle the problem is as follows:

Express the speed (V) of a car given a constant power P , the mass of the car is m, the car travels distance x and it at first was at rest.

I assume initial speed and dist. is zero, if P is constant I can write it as P=FV so
V=P/F ; F=mA (where A is acceleration) here I feel there should be some integration but I don't know how to continue ?

Help will be appreciated!

dextercioby

Why do they give you the distance "x"...?It requires a simple integration.

[tex]P=m\frac{dv}{dt}v [/tex]

Do u see how to derive [itex] v(t) [/itex]...?

Daniel.

sAXIn

No I'm not so good with diff. equations .!

dextercioby

Separate variables and integrate with corresponding limits...

[tex] v \ dv =\frac{P}{m} dt [/tex]

Daniel.

sAXIn

Already made but the answer is given by x ,p ,m and factoring numbers !
I think DX/DT is needed ??/

dextercioby

It can't."x" given in the problem is a number.I don't know why they gave it,though...

Daniel.

sAXIn

I can post the answer for you it goes like : v=(3xp/m)^(1/3)!!!!
The question is from Resnick Physics 1 4th edition chapter 7 problem 52 , I suppose the answer is correct .

dextercioby

Okay the velocity is

[tex] v=\sqrt{\frac{2P}{m}} \sqrt{t} [/tex] (1)

Integrate wrt time & use the initial condition (t=0,x=0) to find

[tex] x=\frac{2}{3}\sqrt{\frac{2P}{m}} \ t^{\frac{3}{2}} [/tex] (2)

Eliminate "t" between (1) & (2) & u'll find your answer.

Daniel.

sAXIn

Thank you very much
I got it , good to know there are wise people out there.