# Homework Help: Particle Motion

1. Mar 31, 2012

### Cbray

1. The problem statement, all variables and given/known data
A particle moves in a straight line away from a fixed point O in the line, such that when its distance from O is x its speed v is given by v=k/x , for some constant k.

(a) show that the particle has a retardation which is inversely proportional to x3

(b) if a,b,c,d are points in that order on the straight line, such that the distances ab, bc, cd are all equal, show that the times taken to travel these successive distances increase in arithmetic progression.

2. Relevant equations
Possible the answer to the first one comes into relevance, -k2*x-3

3. The attempt at a solution
let the four points have x coordinates
x, x+xo , x+2xo , x+3xo

Last edited: Mar 31, 2012
2. Mar 31, 2012

### rock.freak667

For part a) how would you find the retardation ? (negative acceleration)

(Hint: use the chain rule to express 'a' in terms of 'v' and 'x')

For part b) try finding time based on t= distance/velocity at the given points.

3. Apr 1, 2012

### Cbray

I still can't figure it out :L

4. Apr 1, 2012

### rock.freak667

If a=dv/dt, can you use the chain rule to re-write this in terms of v and x? (Hint: you will have to have a dv/dx term)