In designing subway trains and stations, engineers want to optimize the time and energy use between stations. A train can comfortably accelerate at 5 ft/s2 without causing its passengers to fall over. When coasting, the train will slow down at an acceleration of -2 ft/s2. The train begins at rest and must come to a complete stop at the destination. If two train stations are 2 miles apart, determine the fastest time that the train can arrive at the second station given the provided accelerations. Also, determine the maximum velocity obtained. Draw the a-t, v-t, and s-tgraphs for the train. (122 s, 174 ft/s)