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Author Topic: Speeding - Two solutions  (Read 790 times)  Share 

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Speeding - Two solutions
« on: February 05, 2008, 06:31:52 pm »
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This could also go in maths section but whatever.

A speeding motorbike travels past a stationary police car. The police car starts accelerating immediately, and keeps accelerating until it has passed the bike.

DATA: motorbike speed: 35ms-1; police car acceleration: 4ms-2

How far does the police car travel before it overtakes the motorbike?


Ok so there are two ways which I think should work in solving this, but they give different answers.

Solution 1 - Motion Formulae

Motorbike:


Police car:


So or



Solution 2 - Summation

Motorbike:


Police car:


So or



How is it that this can be wrong? Thanks
« Last Edit: February 05, 2008, 06:34:05 pm by DivideBy0 »

Collin Li

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Re: Speeding - Two solutions
« Reply #1 on: February 05, 2008, 09:42:40 pm »
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Summation? I don't know why you think it is correct. It may be flawed because summation is based on being an integer only.

A fast way to do this question, however, would be to draw a velocity-time graph, and then realise that the time taken to reach 35 m/s is seconds. Then, you can now use symmetry and say that in seconds, the total displacement between the car and motorbike will be zero, so that the distance covered will be
« Last Edit: February 05, 2008, 09:44:34 pm by coblin »

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Re: Speeding - Two solutions
« Reply #2 on: February 05, 2008, 10:22:56 pm »
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Thanks coblin, that method is quite good too :)

But are you sure t must be an integer? I mean, for the formula for summation it never says that the upper limit must be an integer, as far as I know.

Collin Li

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Re: Speeding - Two solutions
« Reply #3 on: February 05, 2008, 11:02:32 pm »
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The formula for summation is based on the addition of how many metres is moved per second. The formula is only true for integer values of . It is based on the fact that moves up by increments of 1. What you could do is calculate the first 0.75 seconds, then do the rest from 0.75 to 15.75, or something similar to that - although both of these attempts would be particularly long-winded and difficult to understand.
« Last Edit: February 05, 2008, 11:26:57 pm by coblin »

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Re: Speeding - Two solutions
« Reply #4 on: February 06, 2008, 06:51:19 pm »
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I talked to my physics teacher today and he said that the police car actually travels 2 metres in its first second, and 6 in the next, so the sum should be