Final answer:
Velocity vs. time and acceleration vs. time graphs are created from a position vs. time graph by plotting the slope of the position graph and the slope of the velocity graph respectively. Analyzing these slopes at different intervals helps understand the car's motion, such as constant movement, acceleration, and deceleration.
Step-by-step explanation:
When creating a velocity vs. time graph (v vs. t graph) and an acceleration vs. time graph (a vs. t graph), one must analyze the position vs. time graph provided for the motion of a particle or an object like a car. The slope of the position vs. time graph at any point will give the velocity at that time, which means plotting this slope against time will yield the v vs. t graph.
Similarly, the slope of the v vs. t graph represents the acceleration, which can then be plotted to create the a vs. t graph. To describe the motion of the car, you must interpret these graphs. For example, if the position graph is linear and the slope is positive, the car is moving at a constant velocity. A curved position graph indicates changing velocity, meaning acceleration occurs. Additionally, where the v vs. t graph crosses the time axis, the car is momentarily at rest. Where the a vs. t graph is above the time axis, the car is accelerating, and where it's below, the car is decelerating. Different intervals can be broken down such as 0-2 seconds, 2-4 seconds, and 4-6 seconds to better analyze the motion during specific periods.