# Determine an expression for distance traveled and the time elapsed

1. Jan 21, 2012

### thestiggg

1. The problem statement, all variables and given/known data

A self propelled vehicle of mass m travels in a straight line. The vehicle has an engine which provides constant power P so that the acceleration 'a' at an instant is given by a=P/mv where v is the speed of the vehicle and all frictional resistance is neglected. Determine expressions for:

a) the distance traveled,

b) the time elapsed

2. Relevant equations

a=P/mv

3. The attempt at a solution

I took the derivative of a so,

a=dv/dt then tried to get to v=ds/dt

I ended up with this

ds/dt=sqrt(2p/m + Vo^2)

2. Jan 21, 2012

### tiny-tim

welcome to pf!

hi thestiggg! welcome to pf!
you mean ds/dt=√(2pt/m + vo2) ?

but i suspect the question wants answers to a) and b) as functions of v …

try the standard chain rule trick a = dv/dt = dv/ds ds/dt = v dv/ds

3. Jan 21, 2012

### thestiggg

Yes sorry I missed the t but that's what I meant. I'll give it a try and get back to you

EDIT: and should I integrate and evaluate to v, vo, s and so?

4. Jan 21, 2012

### tiny-tim

yup!

5. Jan 21, 2012

### thestiggg

Is it safe to assume that vo, so is = 0 according to the question?

6. Jan 21, 2012

### thestiggg

Okay so for a) I used "v dv = a ds " and I got " (m/p)*((v2^3-v1^3)/3) + so = s "

For b) I used a=dv/dt and I got " t= (m/p)*((v2^2-v1^2)/2) "

Does that look reasonable?

7. Jan 21, 2012

### tiny-tim

i don't think so

8. Jan 22, 2012

### tiny-tim

oops!

oh i'm sorry!

i was replying to your post #5, i didn't notice your post #6 at all (it came in a few seconds before mine) …
yes, that's fine!

(except for the constants in the first one: you need either a constant s0 or a constant v0, not both!

also, you should use v and v0, not v1 and v2 )