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M3- Trapezium Rule to find speed change

Hi, I was slightly confused as to how to get to part c. The mark scheme does some weird integration to get velocity from acceleration that I don't quite understand.
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(edited 6 years ago)
The working for part (c) is the solution to a separable differential equation. The basis of this is to group all the v terms with dv and all the t terms (if any) with dt, then to integrate the two sides of the equation with respect to t and v respectively.
Original post by student1856
Hi, I was slightly confused as to how to get to part c. The mark scheme does some weird integration to get velocity from acceleration that I don't quite understand.


After separating the variables, the solution uses numerical integration via the trapezium rule - see here, with 2 intervals, for the the second integral.
Reply 3
Original post by ghostwalker
After separating the variables, the solution uses numerical integration via the trapezium rule - see here, with 2 intervals, for the the second integral.


I'm not entirely sure how they integrate 10000v/8000-v^3.
Reply 4
Original post by old_engineer
The working for part (c) is the solution to a separable differential equation. The basis of this is to group all the v terms with dv and all the t terms (if any) with dt, then to integrate the two sides of the equation with respect to t and v respectively.


I'm not sure If my mind is going blank or something, I just can't seem to remember how to integrate 10000v/8000-v^3.
Original post by student1856
I'm not entirely sure how they integrate 10000v/8000-v^3.


They don't integrate it in the normal manner. They use a numerical approximation - have a look at the link I posted.
Reply 6
Original post by ghostwalker
They don't integrate it in the normal manner. They use a numerical approximation - have a look at the link I posted.


I'm sorry if I'm being stubborn, I'm just a little confused as this is the first time I've encountered this method of integration in all my time doing past papers.
Original post by student1856
I'm sorry if I'm being stubborn, I'm just a little confused as this is the first time I've encountered this method of integration in all my time doing past papers.


You should have met it in C2.
Original post by student1856
I'm sorry if I'm being stubborn, I'm just a little confused as this is the first time I've encountered this method of integration in all my time doing past papers.


I've never seen it come up in any mechanics paper.

Here is another link:

here

It's a method of working out a definite integral, without actually doing the integration - it gives you an approximation to the area under the curve.

Google'ing produces quite a bit of info.
(edited 6 years ago)
Original post by ghostwalker
I've never seen it come up in any mechanics paper.



The question above is from Edexcel June 2009. The trapezium rule was also asked for in Edexcel M3 May 2015. It's not unreasonable to ask M3 candidates to use a technique that they learnt in C2.

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