Solve Kinematics Confusion: Motorist vs Police Car

[Exuro89]

Homework Statement

A motorist traveling at a constant speed of 160 km/h in a 50-km/h speed zone passes a parked police car. Three seconds after the car passes, the police car starts off in pursuit. The policeman accelerates at 2m/s^2 up to a speed of 30 m/s, and then continues at this speed until he overtakes the speeding motorist. How long from the time he started does it take the police car to overtake the motorist? The motorist continues at a constant speed during this process.

Homework Equations

X=X_o+V_o*t+.5at^2

The Attempt at a Solution

I'm somewhat confused with how the cop car is suppose to pass the motorist. It says that the motorist is going at a constant 160km/h which is equal to 44.44m/s correct? It then states that when the police car is passed the police car beings to accelerate at 2m/s^2 until a velocity of 30m/s. How could the police car even catch up to the motorist if it isn't going faster than the motorist? Am I reading this problem incorrectly?

 

[SammyS]

Yes, 160 km/hr = 44.44 m/s.

Are you sure it's not 60 km/hr rather than 160 km/hr?

 

[Exuro89]

Yes I'm sure. It was multiple choice and apparently the answer is a negative...

 

[SammyS]

If you blindly plug into the right equations, of course the answer would be negative. Algebra has no way to know how nonsensical that would be.

As you noticed, there is no time in the future when the car would overtake the motorist.

BTW: I suspect that the negative answer is wrong too. It assumes the policeman is traveling backwards during the time the problem states he is stopped.