Acceleration vs. Time
* On the first graph, the man walks slowly to the house from the origin. On the Position-Time graph, the line is a positive consistent rise. This is because his position is going in a positive direction as well as the time is going in a consistent positive direction. On the Velocity-Time graph, the line is straight across at 2 m/s because the velocity does not change because of the consistent speed of the man walking to the house. Since the velocity is constant the acceleration is zero. On the Acceleration-Time graph, the line is flat and straight across at the 0 m/s line because the man does not accelerate. He just walks at a consistent pace to the house. This is called constant speed because there is no variation in his speed.
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A positive slope indicates a changing velocity which is a positive acceleration. On the Acceleration-Time graph, the line constantly rising because the man is running, constantly speeding up.
* On the third example, the man steps outside and walks quickly for 3 meters then he immediately slows down and walks the rest of the way. On the Position-Time graph, the line spikes down quickly then continues in a downward consistent decline. This is because he ran for the first 3 meters then walked at a consistent speed. The reason it is going down is because he is going in the opposite direction. On the Velocity-Time graph, the line starts around the -3m mark and is flat for the first little bit then goes straight up and then straight across again, closer to the zero mark. On the Acceleration-Time graph, the line is flat at first then there is a spike then back down to the starting point and flat across the rest of the graph.
* On the forth example the man walks steadily toward the tree, stops, turns and walks steadily to the house slowing to a stop before he arrives. On the Position-Time graph, there is a consistent decline then a consistent incline. This is because he walked steadily in one direction then turned around and walked steadily in the opposite direction. On the Velocity-Time graph, the line starts below the zero mark and is a flat straight line. It then goes straight up, above the zero line then flattens out and is straight across on the graph. The lines are flat because he is walking at a steady pace in both directions. On the Acceleration-Time graph, the line is flat across the entire graph because even though the man is walking in two different directions, he is walking at the same pace both ways.