(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

(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.

2. Relevant equations

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

3. 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.

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Velocity and distance traveled of a particle

**Physics Forums | Science Articles, Homework Help, Discussion**