Final answer:
To analyze the car's motion, we transform the position vs. time graph into velocity vs. time and acceleration vs. time graphs. This involves examining the slope of the original graph over different intervals, with each segment indicating periods of constant velocity, changing velocity, or no movement.
Step-by-step explanation:
Understanding Motion Through Graphs
Interpreting the motion of a car from a position vs. time graph involves creating corresponding velocity vs. time (v vs. t) and acceleration vs. time (a vs. t) graphs.
The position vs. time graph depicts a simplified model of a car's trip using straight-line segments, implying different motions over defined time intervals.
To create the v vs. t and a vs. t graphs, one must analyze the slope of the position vs. time graph at each section, recognizing that the slope represents the velocity of the car.
In the first section, 0 to 2 seconds, if the position vs. time graph is a straight line with a positive slope, this indicates a constant velocity. Hence, the velocity vs. time graph will be a horizontal line at the slope's value.
Since the velocity is constant, the acceleration is zero, resulting in a horizontal line at zero on the acceleration vs. time graph.
From 2 to 4 seconds, if the slope of the position vs. time graph changes (increases or decreases), this indicates a changing velocity, and thus the velocity graph will either slope up or down accordingly.
The acceleration can be determined by the change in slope over time. Finally, from 4 to 6 seconds, if the slope becomes zero (horizontal), the car has stopped, reflected by a velocity of zero and again, no acceleration.