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cdx

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## Homework Statement

(I can't seem to get the super and subscripts to work so I apologize if this looks ugly.) The position of a particle moving along the x-axis is given at time t by: x = C0 + C1t + C2t^2. At time t = 4.0s the acceleration of the object is a = -20 m/s^2 and that the object passes through the origin x = 0 at t = -2.0s and t = 6.0s. Find the velocity of the particle at t = -2.0s and the maximum value of the distance of the particle from the origin measured in the positive x-direction.

## Homework Equations

x = (0.5)at^2 + v0t + x0

## The Attempt at a Solution

I've tried three approaches: differentiating with respect to the x equation above, integrating from the acceleration given, and setting up x = 0 = (t + 2)(t - 6) from the information given.

Differentiating and integrating lead me to the same problem.. how to find the constant C in v(t) = -20t + C.

Setting up the factor-like problem I obtain t^2 -4t - 12. Looking at this equation I'm led to believe that C2 = 1, C1 = -4, and C0 = -12 from the coefficients. Taking the derivative of this, I get v(t) = 2t - 4. Deriving again I get 2 ms^2 which is not the -20 ms^2 provided.

I'm not sure how to start solving this equation correctly. Could someone point me in the right direction? Thanks.