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

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 \(15 \text{ m/s}\). When the velocities of the particles match, what is their velocity?