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.

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

Do u see how to derive $v(t)$...?

Daniel.

 

[sAXIn]

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

 

[dextercioby]

Separate variables and integrate with corresponding limits...

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

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

$$v=\sqrt{\frac{2P}{m}} \sqrt{t}$$ (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.

 

[sAXIn]

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