![1905[1].jpg](https://i.imgur.com/5svx5LE.jpg "1905[1].jpg")
How was the second integral obtained? What rule was used? Why were we integrating with respect to distance, and then this was switched to integration with respect to momentum (mv)? And was this a def. integral from 0 to s at first, but transformed into a def. integral from 0 to momentum?
pic related
The variable s denotes distance by the way.
Quick google search
https://socratic.org/questions/how-is-momentum-of-an-object-related-to-stopping-distance
>>8033853
[math]\displaystyle \frac{ds}{dt} = v [/math]
>>8033861
I know this already, and I still don't get it. I need a step by step explanation of how the second integral was made to appear.
>>8033869
Thanks, now I understand why they integrated with respect to momentum. But why was the definite integral changed as being from 0 to s to 0 to momentum?
>>8033874
Anyone?
>>8033853
oh my god integration is so friggin gay fuck my ass
>differential and upper bound are the same variable
absolutely disgusting
>>8035133
I think it's an issue of being rigorous. There should be two integrals, one for the range of position (0 to s) and one for momentum (0 to mv). But they just write the one.
Why is it not a definite integral of vd(mv) from to 0 to s? Why is it from 0 to mv?
I got how vd(mv) was obtained from d(mv)/dt ds. But why was the definite integral switched from being from 0 to s to 0 to mv?
>>8035957
Anyone?
>>8036242
what class is this op
also, idk lel
>>8033853
Fucking subscribe to chegg man or type that shit into wolfram. Math is hard, but you can do it with help, also youre not going to use that shit in the field really anyways. If you do, you can look that shit up.
physics really pisses me off sometimes
if it's not some unexpected infinity showing up, it's some asshole textbook author that skips the important steps and just leaves out an integral sign entirely
why does this happen?
>>8037883
>why does this happen?
My professor was telling me they show double/triple integrals as single integrals in textbooks because they don't want to scare students.
>>8037943
are you serious
>>8037883
>>8037529
>>8037193
>>8033853
You guys are tards, i'm a NEET college dropout and even I can see that a) ds/dt =v b) its now summed to momentum because by doing step a) you've set s to be constant and c) they have done this so that they can integrate that final formula from 0 to v only seeing as m or s doesn't show up in it
>>8037970
>able to decipher textbook runes
>NEET dropout
you must hvae good kind of autism, like jacob barneet, or neil degrasse titan
>>8037980
i am extremely autistic.
>>8037994
somebody make this a 4chan banner
>>8037193
Special relativity
