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

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

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

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

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

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

swin2013
 one year 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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