Final answer:
To create velocity and acceleration graphs from a position vs. time graph, identify periods of motion with the same characteristics and determine velocity and acceleration during those intervals. A stationary car has zero velocity and acceleration, while a moving car's graphs show changes over time.
Step-by-step explanation:
The question involves drawing a velocity vs. time (v vs. t) graph and an acceleration vs. time (a vs. t) graph based on a position vs. time graph and describing the motion of a car. Based on the information provided, for a car stationary at home, the v vs. t graph would be a horizontal line at 0 m/s since there is no change in position, and the a vs. t graph would also be a horizontal line at 0 m/s² since there is no change in velocity. For the motion of the car described as accelerating from rest, speeding up and possibly decelerating, the corresponding graphs will display the changes in velocity and acceleration over time. The displacement-time graph for a car that moves with a constant velocity will be a straight line with a constant slope. When the car is accelerating, the graph will show a curve that represents increasing velocity. Lastly, if the car reverses direction, the displacement-time graph will reflect this with a change in slope.