## Problem 6: Three friends, Alex, Luke and Emma, had a bike race. At an instant t=0, Alex was 10 meters ahead of Emma and Luke was 18 meters ahead of her. Alex was biking with a constant speed 6 m/s. Luke had a speed 10 m/s. He was slowing down with acceleration 0.8 m/s2. Emma was trying to catch up with the boys. At an instant t=0, her speed was 5 m/s and her acceleration was 1.2 m/s2. Plot the graphs of motion of three friends and find at what time Emma will catch up Alex and Luke and at what distance from the initial position.

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