Final answer:
The position of a car as a function of time can be described by an expression, x(t), and the velocity and acceleration can be derived from the slope of the position vs. time graph and the rate of change of the velocity, respectively. For constant velocity, the acceleration is zero, and the acceleration vs. time graph is a flat line at zero.
Step-by-step explanation:
The position of a car as a function of time is given by the expression x(t), which represents the car's position at different times. The corresponding velocity vs. time graph can be obtained by calculating the derivative of the position function, giving us the velocity which is the rate of change of position with time. The acceleration vs. time graph is derived from the velocity function by again taking the derivative, which gives us acceleration as the rate of change of velocity with time.
Given the position data of a car at various points in time, to draw the velocity vs. time graph, one would look at the slope of the position vs. time graph, as the slope at any given point represents the car's velocity at that point in time. If the position vs. time graph is a straight line, then the car's velocity is constant, and the velocity vs. time graph will be a horizontal line at the value of that constant velocity. If the position vs. time graph is curved, the velocity changes with time, and the velocity vs. time graph would reflect those changes.
The acceleration vs. time graph shows how the car's velocity changes over time. If the velocity vs. time graph is a straight, horizontal line, it indicates zero acceleration since the car's speed is not changing. If the line slopes upward, the car is accelerating; if it slopes downward, the car is decelerating. These characteristics would be represented as a flat line at zero for constant velocity, or as positive/negative values for acceleration/deceleration on the acceleration vs. time graph.