# Particles math problem

1. Jan 29, 2009

### movanes

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

A particle leaves its initial position x0 at time t=0 moving in the positive x direction with speed v0 but undergoing acceleration of magnitude a in the negative x direction. Find expressions for 1) the time when it returns to its initial position and 2)the speed when it passes that point.

2. Relevant equations

3. The attempt at a solution
Wouldn't it stop first before returning to its initial position? Is it relevant that 2(xf-x0) is the total distance to return?

2. Jan 29, 2009

### Dick

Re: particles

Sure it will stop before returning. No, the total distance isn't terribly relevant. Unless you know a formula that involves it. You left the "Relevant Formulas" section blank. You know the second derivative of x(t) with respect to t is the acceleration 'a'. Can you either i) integrate that equation or ii) do you know a formula for the displacement of a particle under uniform acceleration?