SPM 2017 Add Maths Paper 2, Question 12Kinematics of Linear Motion

Diagram 7 shows the initial position and direction of motion of particle P and particle Q. Both particles start moving simultaneously. O and L are 11 m apart, with P starting at O moving toward L, and Q starting at L moving toward O. The velocity of particle P, vp m/s, is given by vp = 9t² + 10 and the displacement of particle Q, sQ m, from point L is given by sQ = 3t³ - t, where t is time in seconds after particle P passes point O and particle Q passes point L. (a) Find the initial velocity, in m/s, of particle Q. (b) Find the total distance, in m, travelled by particle Q in the first 2 seconds. (c) Calculate the distance, in m, of the particles from point L when particle P and particle Q meet.