Particle P P\,P passes a point O O\,O with speed 6 m s-1 and then moves along a straight line with constant acceleration 2 m s-2. Four seconds later, particle Q Q\,Q passes O O\,O moving in the same direction with constant speed 30 m s-1.
Let t t\,t seconds be the time after P P\,P passes OOO.
Show that, when the particles are at the same point, t2−24t+120=0t^2-24t+120=0t2−24t+120=0.
Hence show that Q Q\,Q overtakes P P\,P twice.
Determine the distance from O O\,O at which Q Q\,Q first overtakes PPP.