A motorcycle is following a car that is traveling at constant speed on a straight highway. Initially, the car and the motorcycle are both traveling at the same speed of 46.0 mph, and the distance between them is 54.0 m. After t_1 = 2.00 s, the motorcycle starts to accelerate at a rate of 8.00 {m/s^2}. The motorcycle catches up with the car at some time t_2.
How long does it take from the moment when the motorcycle starts to accelerate until it catches up with the car? In other words, find t_2-t_1.
How far does the motorcycle travel from the moment it starts to accelerate (at time t_1) until it catches up with the car (at time t_2)?