## Constant Power and speed of particle relation

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!
 Blog Entries: 9 Recognitions: Homework Help Science Advisor Why do they give you the distance "x"...?It requires a simple integration. $$P=m\frac{dv}{dt}v$$ Do u see how to derive $v(t)$...? Daniel.
 No I'm not so good with diff. equations .!

Blog Entries: 9
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Homework Help

## Constant Power and speed of particle relation

Separate variables and integrate with corresponding limits...

$$v \ dv =\frac{P}{m} dt$$

Daniel.
 Already made but the answer is given by x ,p ,m and factoring numbers ! I think DX/DT is needed ??/
 Blog Entries: 9 Recognitions: Homework Help Science Advisor It can't."x" given in the problem is a number.I don't know why they gave it,though... Daniel.
 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 .
 Blog Entries: 9 Recognitions: Homework Help Science Advisor Okay the velocity is $$v=\sqrt{\frac{2P}{m}} \sqrt{t}$$ (1) Integrate wrt time & use the initial condition (t=0,x=0) to find $$x=\frac{2}{3}\sqrt{\frac{2P}{m}} \ t^{\frac{3}{2}}$$ (2) Eliminate "t" between (1) & (2) & u'll find your answer. Daniel.
 Thank you very much I got it , good to know there are wise people out there.