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swin2013
 2 years ago
A particle starts at x(0) = 2. If its velocity is given by v(t) = ln(1+t), find its position at t = 5
swin2013
 2 years ago
A particle starts at x(0) = 2. If its velocity is given by v(t) = ln(1+t), find its position at t = 5

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CanadianAsian
 2 years ago
Best ResponseYou've already chosen the best response.1Take the integral of velocity from 0 to 5 and then add 2. \[\int\limits_{0}^{5} \ln(1+t) dt\] Set u = 1+t, du = dt So you have \[\int\limits_{0}^{5}\ln(u)du\] Which becomes [uln(u)  u] from 0 to 5 Plug in your values to get 5(ln(5)  1) Then add 2, so the position at t =5 is 2 + 5(ln(5) 1)

swin2013
 2 years ago
Best ResponseYou've already chosen the best response.0is there a way to find it without u substitution?

CanadianAsian
 2 years ago
Best ResponseYou've already chosen the best response.1Nope. It's the only way to do that sort of integral unfortunately.

swin2013
 2 years ago
Best ResponseYou've already chosen the best response.0really? oh I thought you can use it with FTC

CanadianAsian
 2 years ago
Best ResponseYou've already chosen the best response.1The FTC states that if you have a function F(x) which is the integral of another function G(x) then the derivative of F(x) is simply G(x). Additionally, the integral of G(x) is just F(b)  F(a).

swin2013
 2 years ago
Best ResponseYou've already chosen the best response.0oh kinda like if it's F'(x) = f(x)?

swin2013
 2 years ago
Best ResponseYou've already chosen the best response.0but wait, isn't u supposed to be ln (u) and du is 1+t? because when i plug in your answer, there is no answer choices for it :/

swin2013
 2 years ago
Best ResponseYou've already chosen the best response.0from your answer it is 5.047 correct?

CanadianAsian
 2 years ago
Best ResponseYou've already chosen the best response.1Ugh, sorry, it's been a long day. (ulnu  u) from 0 to 5 should be (1 + t)(ln(1+t)  1) so it's actually 6(ln6 1).

CanadianAsian
 2 years ago
Best ResponseYou've already chosen the best response.1Because u was substituted for 1+t earlier, so we need to exchange it back out.

swin2013
 2 years ago
Best ResponseYou've already chosen the best response.0i keep getting 9.65 but it is not an answer choice? i think there's a step missing or a miscalculation :( the answer choices are : a) 5.751 b) 7.751 c) 1.792 d) 3.792 e) 3.751

CanadianAsian
 2 years ago
Best ResponseYou've already chosen the best response.1Geezus, I just reread my work and I made another mistake. Sorry D: So when you put 1+t back in for u you get (1+t)(ln(1+t) 1) from 0 to 5. So when you put these values in, you get: 6(ln6 1)  1(ln1 1) Which gives you the distance traveled. BUT you still have to add 2 to the answer, which will give you the position. So the answer should be B.

swin2013
 2 years ago
Best ResponseYou've already chosen the best response.0i'm confused on the 1ln (11) part. i'm sorry lol

swin2013
 2 years ago
Best ResponseYou've already chosen the best response.0@CanadianAsian can you please dissect the derivative section? sorry for asking lol
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