(1) Cars move in a straight line. (2) The acceleration of the i-th car is directly proportional to the difference between the speeds of the i-th car and the (i-1) -th car. (3) The constant of proportionality for all expressions found in the previous subsection is the same. (4) All cars start from rest. That is, the initial velocities of all cars is: 0 m/s (5) The speed of the first car is given by the function: v1 (t) = t m/s Considering the hypotheses and assuming that the system involves 5 cars It only responds to the following items: (a) Build and solve the mathematical model that describes the system. (b) Consider that the initial position of the first car is x1 (0) = 0 meters, for: (b.1) Determine the position functions for all cars. (b.2) Determine the starting positions of the rest of the cars. (1) Cars move in a straight line. (2) The acceleration of the i-th car is directly proportional to the difference between the speeds of the i-th car and the (i-1) -th car. (3) The constant of proportionality for all expressions found in the previous subsection is the same. (4) All cars start from rest. That is, the initial velocities of all cars is: 0 m/s (5) The speed of the first car is given by the function: v1 (t) = t m/s Considering the hypotheses and assuming that the system involves 5 cars It only responds to the following items: (a) Build and solve the mathematical model that describes the system. (b) Consider that the initial position of the first car is x1 (0) = 0 meters, for: (b.1) Determine the position functions for all cars. (b.2) Determine the starting positions of the rest of the cars