SOLUTION: Please help me with this problem: A particle moves along the x axis so that its velocity at time t, t > 0, is given by v(t) = {{{(t - 2)/t}}}. If the particle's position at t = 1

Algebra ->  Test -> SOLUTION: Please help me with this problem: A particle moves along the x axis so that its velocity at time t, t > 0, is given by v(t) = {{{(t - 2)/t}}}. If the particle's position at t = 1       Log On


   

Question 1033818: Please help me with this problem:
A particle moves along the x axis so that its velocity at time t, t > 0, is given by v(t) = %28t+-+2%29%2Ft. If the particle's position at t = 1 is x = 10, write an equation which describes the position of the particle as a function of t.
Also, what velocity does the particle approach as t get large?
Found 2 solutions by Fombitz, robertb:
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
To find the position, integrate the velocity.
v%28t%29=1-2%2Ft
So then,
x%28t%29=int%28%28v%28t%29%29%2Cdt%29
x%28t%29=int%28%281-2%2Ft%29%2Cdt%29
x%28t%29=t-ln%28t%29%2BC
So when t=1,
1-ln%281%29%2BC=10
1%2BC=10
C=9
highlight%28x%28t%29=t-ln%28t%29%2B9%29
.
.
When t-%3Einfinity,
v%28t%29=1-0
v%28t%29=1

Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
x%28t%29+=+t-2lnt%2BC ==> x%281%29++=+10+=+1-2ln1%2BC ==> C = 9.
==> x%28t%29+=+t-2lnt%2B9