The Time of Return for a Particle Undergoing Negative Acceleration

AI Thread Summary
To determine when a particle undergoing negative acceleration returns to its initial position x_0, the relevant equations are v = v_0 - at and x = x_0 + v_0*t. The correct approach involves using the equation x = x_0 + v_0*t + 0.5*a*t^2 to account for the acceleration. Setting x equal to x_0 leads to a quadratic equation, yielding two solutions: t = 0 and another positive time value. This second solution represents the time at which the particle returns to its starting position.
estie
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Homework Statement



A particle leaves its initial position x_0 at time t=0 moving in the positive x direction with speed v_0 but undergoing acceleration of magnitude a in the negative x direction. Find expressions for (a) the time when it returns to the position x_0.

Homework Equations



v=v_0-at
x=x_0+v_0*t

The Attempt at a Solution



i know that v=v_0, but that gives me a time of 0, which doesn't make sense. I'm also not supposed to use x_0 in the solution. otherwise, i think the solution should be (v-v_0)/-a.
 
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x=x_0+v_0*t
This formula is for uniform motion (zero acceleration).
You need to use x = Vo*t + .5*a*t^2.
When you set x = 0, you will have a quadratic equation with two solutions. One will be t=0 of course and the other greater than zero.
 

Homework Equations



v=v_0-at
x=x_0+v_0*t
By the way estie, if you wish to use TeX-style notation on this forum you can wrap [ tex] [/tex] tags around your equations so it'll look more like this:
x=x_0+v_{0}t<br />

Welcome to PF!
 
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