Final answer:
The question pertains to linear distance equations used in physics or mathematics to describe motion. Such equations represent relationships between distance and time and are part of kinematic studies.
Step-by-step explanation:
The student appears to be dealing with distance equations in the context of physics or mathematics. These equations, such as Josiah's Distance Equation, represent linear relationships between distance and time. They are foundational in kinematics, a branch of mechanics that describes the motion of objects without considering the causes of motion.
Using the format d(t) = at + b, the equation pertains to the motion of an object with an initial position (when t=0) specified by b, and a rate of change of position (velocity) specified by a. If we were to relate this to the fourth kinematic equation, when an object starts from the origin and at rest, the equation reduces to d = (1/2)at², where a is the acceleration and t is the time elapsed. To answer the question of finding the distance, you would use known values for acceleration and time.
For example, if the displacement is given as 2.00 km for part (a), then the equation d(t) = 4t + 12 could be used to find the time t when the displacement occurs, thus solving for the distance traveled.