Chapter 9, Problem 39P

Consider a system of three equal-mass particles moving in a plane; their positions are given by $a_i\hat{i}+b_i\hat{j}$, where a_i and b_i are functions of time with the units of position. Particle 1 has a₁ = 6t² + 5 and b₁ = 0; particle 2 has a₂ = 4t + 3 and b₂ = 4t; particle 3 has a₃ = 8t and b₃ = t + 4. Find the center-of-mass position, velocity, and acceleration of the system as functions of time.