A particle of mass 1.5kg moves along a straight line with an initial velocity of 4ms−1. During the interval 0≤t≤2s it is subjected to a variable force given by F(t)=6t2N; after t=2s no external force acts on the particle.
a. (i) Derive an expression for the particle’s momentum as a function of time in the range 0≤t≤2s.
b. (ii) Find the instant within this interval at which the momentum of the particle becomes exactly twice its initial value.
c. (iii) Calculate the displacement of the particle during the time interval 2s≤t≤5s.