SPM 2019 Add Maths Paper 2, Question 12Kinematics of Linear Motion

Solution by graph sketching is not accepted. A particle moves along a straight line such that its velocity, v ms⁻¹, is given by v = t³ - 4t² + 3t, where t is time, in seconds, after passing through a fixed point O. Find (a) the initial acceleration, in ms⁻², of the particle, (b) the time interval, in seconds, when the acceleration of the particle is less than 6 ms⁻², (c) the time, in seconds, when the particle stops instantaneously, (d) the total distance, in m, travelled by the particle until the particle returned to the fixed point O for the second time.