motion

[tolga]

a car is travelling at a constant speed of 80km/h passes a stationary motorcycle policeman. The policeman sets off in pursuit,accelerating uniformly to 80km/h in 10s and reaching a constant speed of 100km/h after a further 5s. At what time will the policeman catch up with the car?
 
i know the car is x=v.t , v=22.22m/s but for the police i do x=1/2(27.77)15 but the answer a get is 9.4s where as the real answer is 33s

[Aden]

I like to imagine a speed vs. time graph for these sorts of questions, where the area is the distance. You have to realize that the time taken for the policeman to catch up is ‘x’ and that the policeman isn't just constantly accelerating; he gets to 100km/hr in two parts: first to 80km/hr in ten seconds and then to 100km/hr in another five. To find ‘x’, we need to find when both their distances traveled are equal (I think that is what you’re trying to do as well).

*We'll just say 80km/hr = 22.22m/s and 100km/hr = 27.78m/s

The car’s distance is easier to calculate as it is moving at a constant speed, so it is:
(distance = speed x time)

The policeman’s distance is slightly harder:
His distance from 0s-10s on the speed vs. time graph is marked by a triangle, so the distance for this section is:
His distance from 10s-15s on the speed vs. time graph is marked by a sort of trapezium, so the distance for this section is:
And lastly, his distance from 15 seconds to the unknown 'x' seconds is:

From here, you have an overall equation that looks like this:





Sorry if this looks a bit cluttered, I'm a bit inexperienced with this...

[tolga]

shouldn't x be t and for the last part shouldn't it be (t+15)

[Aden]

Sorry, I called the variable for time as 'x' instead of 't'. It is (x-15) instead of (x+15) since the policeman has already spent 15 seconds accelerating to 100km/hr (you've already calculated the distance for those 15 seconds as 125m and 111.11m). If you look at the graph, the distance traveled after 15 seconds would be (100/3.6)*(x-15). Remember that 'x' is the time when the policeman catches up to the car.

[Greggler]

lol i stuffed this question up by not converting k/ph to m/s LOL!