1. Consider a car "STOP" sign. A certain distance ahead of the car a bike is at rest. Afterwards the car and the bike begin to speed up. The car moves from rest to 85.0 mi/h with constant acceleration 13.4 mi/h-5. The cyclist speeds up from rest to 23.0 mi/h with its speed and position given by the equations v=17.13(1 -e-050)meters/s and. x=17.13(t + 2e-050 )meters. Each vehicle maintains constant velocity after reaching its cruising speed. a. On a sheet of 8.5'x11" Quad-ruled paper (also known as graph paper), CAREFULLY AND ACCURATELY graph by hand the position of both vehicles (in meters) as a function of time (you must show tables of the points you plotted for credit). Use the graph to estimate the time interval (how many seconds) the bicycle is ahead of the car. Your estimate must be obtained directly from the graph. Attach your graph and make sure to show how you estimated these values on the graph itself in addition to writing your estimated values on the graph. Points will be docked for graphs that are too small or too sloppy. b. Accurately plot the difference in their positions as a function of time to determine maximum distance the bicycle leads the car