A particle moves along the x-axis so that at any time t0, its acceleration is given by a(t)=ln(1+2^t). If the velocity of the particle is 2 at time t=1, then what is the velocity of the particle at time t=2?

Question

A particle moves along the x-axis so that at any time t>0, its acceleration is given by a(t)=ln(1+2^t). If the velocity of the particle is 2 at time t=1, then what is the velocity of the particle at time t=2?

liizzyliizz · Answer

so i know the answer is 3.346 but my work is sloppy, and im not sure why i was getting 1.609 instead. help?

anonymous · Answer

$$\int ln(1+2^t)dt$$

see what you get and plug in conditions given

anonymous · Answer

but that's not easy integral

liizzyliizz · Answer

i got some crazy answer on my calculator.... O.O idk what i did wrong

anonymous · Answer

I feel you liz, you can't integrate that problem with what dr.S taught us... :C

liizzyliizz · Answer

when i did it i got 1.609 after a long process.

liizzyliizz · Answer

how is it 3.346 O.O

anonymous · Answer

I am interested to see how you integtated that

anonymous · Answer

did you get the constant? and how did you end up with a number?

liizzyliizz · Answer

i think i started right i plugged in, but then i got lost and did some crazy things, and integrated on ym calculator and then got 1.609

anonymous · Answer

O.o what exactly did you type in because when I put it in all it gave me was the equation again, and how did you plug anything in without the integral?

liizzyliizz · Answer

i used definite integrals.

anonymous · Answer

como?