To determine how fast the police car must go to catch the holdup car, it is essential to calculate the distance traveled by the holdup car during its head start. The holdup car travels at 120 km/h for 1.5 hours, covering a distance of 180 km. The police car must cover this distance in 1 hour, meaning it needs to travel at a speed of 180 km/h. The discussion emphasizes the importance of understanding relative motion and constant speed in solving the problem. This approach clarifies the necessary calculations for determining the police car's required speed.