This is Juliet (as you all know)! And my friend Jensen. We were all taking the bus to Ala Moana Center last Summer, which took about 30 minutes total; 10 minutes waiting for the bus to arrive, and 20 minutes actually riding it including the numerous stops it would come to. Our starting point would be the bus stop directly across from Punahou School and our ending point would be at Ala Moana Center's entrance near Nordstrom. If i were to graph this on an x(distance in miles) vs. t (time in minutes) graph, it would start off as a straight line since we would wait for a certain amount of time for the bus to arrive, then the slope would increase since we are travelling in a direction away from our starting point. At each turn, stoplight, and necessary bus stop, the graph would create a horizontal line (even if it's short) since it accelerates through the gas, brakes, and turning, but the slop would still increase with distance and time because of their direct relationship. Once it has reached the ending point (Ala Moana) the distance travelled would be about 1.5 miles. It would continue travelling its route, and then the slope would begin to turn negative since it is travelling in the opposite direction than before. It would reach the point at which it started, so the distance travelled altogether would be about 3 miles, but the displacement would be 0 miles because it has returned to the same spot.

Compared to walking, the times don't vary by much. If I were to graph walking to Ala Moana, the graph would start off with an automatic incline since there is no need for waiting or resting time, with the exception of crosswalks, since we would just travel straight there. We would be moving at a constant speed in a positive direction away from the starting point if we were to use the same bus stop as the origin of the graph. Travelling with constant speed will take about 30 minutes. Crosswalks and stoplights would alter the graph a little creating a flatline for a couple seconds, but the slop would then increase as we travel farther away from Punahou. Travelling back to Punahou would take the same amount of time and would create a similar slope to that of the bus, but a steeper one since the bus route is farther and in a different direction. Ending up at the bus spot outside of Punahou would still give me a displacement of 0 miles for both the bus and on foot. If I compared the bus time and walking time, they would take about the same amount of time (30 min, but their graphs would show up different with varying resting point and acceleration points.