A particle with velocity at any time t given by v(t)=2e^(2t) moves in a straight line. How far does the particle travel during the time interval when its velocity increases from 2 to 4.
A) 1
B) 2
C) 3
D) e^4
E) e^8-e^4

Question

A particle with velocity at any time t given by v(t)=2e^(2t) moves in a straight line. How far does the particle travel during the time interval when its velocity increases from 2 to 4.
A) 1
B) 2
C) 3
D) e^4
E) e^8-e^4

peachpi · Answer

Integrate v(t) from 2 to 4

bmk614 · Answer

That is what I did, and I got E, but the answer is A

peachpi · Answer

I got E as well

irishboy123 · Answer

" when its velocity increases from 2 to 4."

irishboy123 · Answer

ie

not $2 \le t \le 4$

peachpi · Answer

I see. so you have to solve for the t

bmk614 · Answer

So what do I do?

irishboy123 · Answer

get $t_1$ from $v(t)=2e^{2t} = 2$

get $t_2$ from $v(t)=2e^{2t} = 4$

bmk614 · Answer

I got 
$$t _{1}=0, t_2=\ln(2)/2$$

bmk614 · Answer

So t_1-t_2 doesnt equal 1

irishboy123 · Answer

$t_1 = 0$

$v(t) = 4  \implies  \ln \sqrt{2}$ 

we agree

so now do the integration

bmk614 · Answer

wouldnt it be ln(2)/2

irishboy123 · Answer

yes  $ln(2)/2 = \ln \sqrt{2}$

so we have:
$\Large \int\limits_{0}^{\ln \sqrt{2} } ~ 2 e^{2t} ~ dt$

are you happy with that?

bmk614 · Answer

I plugged that into my calculator and got 1... Thank you so much!

irishboy123 · Answer

hope it's right :-))

lol!!

bmk614 · Answer

Well it gave me the right answer, so I think so haha.