Acceleration overcoming Velocity. Over what time frame?

[Maiton]

Homework Statement

A particle leaves its initial position Xo at time t=0, moving in the positive x direction with speed Vo but undergoing acceleration a in the negative x-direction. Find expression for (a) the time when it returns to Xo and (b) its speed when it passes that point



I'm having difficulting finding my second time t2. If I have this I can find the speed with V=(X-Xo)/(t-0). I'm trying to get into this course but am drawing a blank at this time. If someone could give me a few words in an explanation, I'd be greatly appreciative. It may just open my eyes.

Mike

 

[voko]

You can't get speed with V=(X-Xo)/(t-0). The speed is not constant, there is acceleration. How does speed depend on time under constant acceleration?

 

[vela]

What have you tried to find t₂?