Quick Motion Question - Rejogging memory after a while.

[AviationFanBoy]

Homework Statement

A car traveling with a constant speed of 80km/hr passes a stationary motorcycle policeman. The policeman sets off in pursuit, accelerating uniformly to 80km/hr in 10 seconds and reaching a constant speed of 100km/hr in a further 5 secs. At what time will the policeman catch up with the car.

Homework Equations

N/A

The Attempt at a Solution

I figure if they catch up to each other, then assuming they began from the same point then their displacement will be equal to each other. Thus I did, the speeding car was doing 80km in one hour, and the cop was doing 100 km in one hour. Thus the cop would reach 80km displacement in 48 mins. (0.8 x 60 mins)

 

[haruspex]

the cop would reach 80km displacement in 48 mins.

How did you determine that 80km was the appropriate displacement?
Hint: how much lead does the motorist have when the cop first reaches 100km/h?

 

[AviationFanBoy]

15 secs before he reaches 100km/hr. So then what?

 

[haruspex]

15 secs before he reaches 100km/hr. So then what?

I mean lead as a distance.

 

[AviationFanBoy]

I mean lead as a distance.

333m. As 80km/hr = 22m/s (80/3.6) = 22m/s.
Thus, 15 secs = 333.3 (infinite) meters.

 

[haruspex]

333m. As 80km/hr = 22m/s (80/3.6) = 22m/s.
Thus, 15 secs = 333.3 (infinite) meters.

That's how far the car goes in 15 seconds, but the cop is not standing still.

 

[AviationFanBoy]

That's how far the car goes in 15 seconds, but the cop is not standing still.

The car has a 333m lead over the policeman. Thats what you asked?

 

[haruspex]

The car has a 333m lead over the policeman. Thats what you asked?

333m is the lead he would have had if the policeman had not given chase. Where is the cop after 15 seconds?

 

[AviationFanBoy]

After 15 seconds he is traveling at 100 km/hr and has traveled 360m. As for the first 10 seconds he covers 222m as he is traveling at 80km/hr, and for the next 5 seconds he travels at 100km/hr covering 138m thus after 15 secs the cop is 360meters from the starting position.

 

[haruspex]

As for the first 10 seconds he covers 222m as he is traveling at 80km/hr.

No he isn't - read the question again.

 

[AviationFanBoy]

Sorry, he covers 416 meters in the 15 seconds. As 100/3.6 = 27.8 x15 = ~416m.

 

[haruspex]

Sorry, he covers 416 meters in the 15 seconds. As 100/3.6 = 27.8 x15 = ~416m.

Pay attention! The cop is not moving at uniform speed. For the first 10 seconds he accelerates uniformly from 0 to 80km/h. Do you know the SUVAT equations? These can be used for uniform (i.e. constant) acceleration.

 

[AviationFanBoy]

Yes, i know them. How are they linked though. I reliaze he accelerates at different rates from 0 to 10 then 10 to 15 seconds. Hence why I said, After 15 seconds he is traveling at 100 km/hr and has traveled 360m. As for the first 10 seconds he covers 222m as he is traveling at 80km/hr, and for the next 5 seconds he travels at 100km/hr covering 138m thus after 15 secs the cop is 360meters from the starting position.

 

[haruspex]

As for the first 10 seconds he covers 222m as he is traveling at 80km/hr

No he isn't! Why do you keep asserting that when I have already pointed out that it is wrong?
He starts at 0 km/h, and only reaches 80km/h at the end of the 10 seconds. He does not travel at 80km/h for 10 seconds.
In the usual form, there are five SUVAT equations, each involving four variables. Typically, you know the value of three, and you want to find a fourth, so pick the equation that involves those four variables.
What three values do you know here? What other variable do you want to determine? Which equation should you use?