Halliday, Resnick & Walker — Motion Along a Straight Line: Problem 70

Two particles move along an x axis. The position of particle 1 is given by \( x = 6.00t^2 + 3.00t + 2.00 \) (in meters and seconds); the acceleration of particle 2 is given by \( a = -8.00t \) (in meters per second squared and seconds) and, at \( t = 0 \), its velocity is \( 20 \text{ m/s} \). When the velocities of the particles match, what is their velocity?