Non-constant acceleration not sure how to solve

[anthonytw]

I'm not certain how to solve this, as the acceleration is not constant and dependent on the velocity. Here's the problem:

The acceleration of a marble in a certain fluid is proportional to the speed of the marble squared, and is given (in SI units) by a = -3.10v^2 for v > 0. If the marble enters this fluid with a speed of 1.35 m/s, how long will it take before the marble's speed is reduced to half of its initial value?

I take it I need to integrate the acceleration function, but I don't know how when I have dv/dt = -3.10 (dx/dt)^2. As this is just an introductory physics class and we are barely two weeks in, I'm wondering if there's not a simpler way to look at this. Any help pushing me in the right direction would be extremely appreciated!

 

[Gamma]

dv/dt = -3.10 (dx/dt)^2.

You have complecated the problem by writing v = dx/dt.

You need a differential equation, witch connects v and t.

Leave v as it is and write a = dv/dt. You have a simple integral to do.

Hope this helps,


Gamma.

 

[anthonytw]

I haven't learned differential equations yet. Is there no other way to solve it? I tried moving the v and dv to one side and the constant and dt to the other and solving it like that, but that didn't work..

 

[anthonytw]

Nevermind, I got it using the method I said didn't work above.

 

[Signifier]

Is the answer about 0.239 seconds? (sorry, heh, but I'm trying to immerse myself in physics and I want to check my work)

 

[NEWO]

Your differential equation comes in the form of a simple harmonic motion.

d^2x/dx^2-bdv/dt=0 is the equation you need to solve i think

you will get something like x=bAsin{wt} I think but don't quote me on this where b is the -3.10

you should be then able to change it around to get your answer

 

[Gamma]

a = -3.10v^2

dv/dt = -kv^2 (k=3.10)

separation of variables,



dv/v^2 = -kdt

-1/v = -kt +C

No sinusidal solution.

 

[NEWO]

ahhhh yes you are right

i apologise i thought there was something wrong