Very easy Mechanics Question PLEASE HELP!! (1 Viewer)

[kman16]

okay now this is a very simple question, yet i feel like killing someone because im not getting the answer out.
Q: A particle moves in a straight line away from a fixed point O in the line, such that at time t its displacement from O is x and its velocity is v. At time t=0, x=0, v=V. Subsequently the particle is slowing down at a rate proportional to the square of its speed. Find an expression for the velocity v in terms of displacement x.

What i did was v.dv/dx = -kv^2
and then work from there... i ended up with v = e^-kx + V

PLEASE HELP ME AS IM NOT SURE WHAT I DID WRONG!! D:

Thanks

 

[pokka]

okay now this is a very simple question, yet i feel like killing someone because im not getting the answer out.
Q: A particle moves in a straight line away from a fixed point O in the line, such that at time t its displacement from O is x and its velocity is v. At time t=0, x=0, v=V. Subsequently the particle is slowing down at a rate proportional to the square of its speed. Find an expression for the velocity v in terms of displacement x.
What i did was v.dv/dx = -kv^2
and then work from there... i ended up with v = e^-kt + V

PLEASE HELP ME AS IM NOT SURE WHAT I DID WRONG!! D:

Thanks

The question did not ask for an equation involving "t" so you should NOT include it at all. When you come to step after integrating and have to find the constant C, only use the x and v conditions (NOT "t").

 

[kman16]

The question did not ask for an equation involving "t" so you should NOT include it at all. When you come to step after integrating and have to find the constant C, only use the x and v conditions (NOT "t").

i made a mistake... i came up with: v = e^-kx + V
lol sorry

 

[pokka]

you should have this step in your working out: so when you exponentiate everything to find v, you have: Now that expression should not be equal to so check your working out from there.

 

[kman16]

thank you so much... straight away i can see what i did wrong
i got to that step and then exponentiated each term instead of each side *facepalm durpetydurp