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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
 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
 one year ago

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CanadianAsianBest ResponseYou've already chosen the best response.1
Take 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)
 one year ago

swin2013Best ResponseYou've already chosen the best response.0
is there a way to find it without u substitution?
 one year ago

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

swin2013Best ResponseYou've already chosen the best response.0
really? oh I thought you can use it with FTC
 one year ago

CanadianAsianBest ResponseYou've already chosen the best response.1
The 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).
 one year ago

swin2013Best ResponseYou've already chosen the best response.0
oh kinda like if it's F'(x) = f(x)?
 one year ago

swin2013Best ResponseYou've already chosen the best response.0
but 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 :/
 one year ago

swin2013Best ResponseYou've already chosen the best response.0
from your answer it is 5.047 correct?
 one year ago

CanadianAsianBest ResponseYou've already chosen the best response.1
Ugh, 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).
 one year ago

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

swin2013Best ResponseYou've already chosen the best response.0
i 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
 one year ago

CanadianAsianBest ResponseYou've already chosen the best response.1
Geezus, 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.
 one year ago

swin2013Best ResponseYou've already chosen the best response.0
i'm confused on the 1ln (11) part. i'm sorry lol
 one year ago

swin2013Best ResponseYou've already chosen the best response.0
@CanadianAsian can you please dissect the derivative section? sorry for asking lol
 one year ago
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