Physics ch 2 last h/w

Question

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 50.0 m. After t_1 = 5.00 s, the motorcycle starts to accelerate at a rate of 5.00 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)?

Answer 1

Relative to the car, the motorcycle has to cover 50m in the required time t starting from rest and accelerating at 5.00 m/s^2.

46.0 mi/hr = 46 * 22 / 15 ft/sec.

= 46 * (22 / 15) * 0.3048

= 20.56 m/sec.

50 = 5.00t^2 / 2

t = 4.47 sec.

In time t, the car travels 20.56t m.

The bike travels an additional 50m, making its distance:

20.56 * 4.47 + 50

= 142m.