Can Police Catch the Speeding Motorist?

[aflowernamedu]

How would I solve this?

2 police officers are standing on a road. A motorist comes at 108km/hr(30m/s) The police take 2 s to assess the situation. Then their patrol car accelerates at 2.5m/s^2 for 15s after the 2s and then continues at uniform speed. How far from the observation point does the intersection take place? Assume the motorist maintains a constant speed of 108km/hr?

 

[Bowenwww]

Yes you do, assuming the question means the police react as the bike passes parallel to them.

using:

S = ut + 1/2*a*t²

You find that the police travel 281.25m in the 15 seconds they accelerate, plus the 2 seconds they waited, so in 17s they have traveled 281.25m and accelerated to a constant velocity of 37.5m/s

In this time the motorbike has traveled 17*30 = 510m so the police after 17s are a distance of 228.75m behind the bike

The relative speed between the two is 7.5m/s

So how long does it take to make up 228.75m at 7.5 m/s?

228.75 / 7.5 = 30.5s

plus the original 17s

30.5 + 17 = 47.5s until the police are level with the biker.

 

[aflowernamedu]

Thank you ,but I still am not sure of the answer to "how far from the observation point did the intersection take place?"