Particle Motion with Constant Acceleration: Solving for Time and Speed

[movanes]

Homework Statement

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.

Homework Equations

The Attempt at a Solution

Wouldn't it stop first before returning to its initial position? Is it relevant that 2(x_f-x₀) is the total distance to return?

 

[Dick]

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?