:smile: Alright then!
After integration the equation becomes:
t = -m/2 * ( ln[v_2] - ln[v_1] )
Substituting, m = 10 kg, v_1 = 10 m/s and v_2 = 5 m/s gives t ≈ 3.47 s
Seems plausible, right?
Uhm, I don't get it :(
How do you get rid of the m/2 inside d(mv2/2) so you're left with just d(v2)?But if you do it the other way:
write d(mv2/2) as mv dv..
then the equation becomes m/-2v dv = dtis that correct? oh man I really should start polishing up those calculus skills :)
Okay, then:
case i]
Write 1/(-2v2) * d(mv2/2) = dt as
1/(-4v2/m) d(v2) = dt
Then integrate the left side from v_1 to v_2 (substitute values) and the right side becomes t, obviously and then you've got an answer, right?and if you go for ii] then the equation becomes:
m/-2v dv = dt
and...
oooh, sorry
write it as:
1/(-2v2) * d(mv2/2) = dt
THEN integrate both sides right?
But how do I integrate with respect to mv2/2 when the variable on the left side is just v?
Thanks tiny-tim!
So you get:
d(mv2/2)/dt = -2v2
d(mv2/2) = -2v2 dt
integrate both sides: d(mv2/2) was -375 J
-375 = -2v2*t
Uhm, how exactly do I continue from here?
Hi Forum :)
This is not a specific homework problem, just something I tried to solve myself.
Homework Statement
A 10 kg object is moving at 10 m/s.
The object is losing 2v^2 J of kinetic energy per second.
Determine the time it takes for the speed to decrease from v_1 = 10 m/s to v_2 = 5...