Kinematic Problem: How Long to Reach Half Speed in a Fluid?

[bjon-07]

Hi all, can some one please help me on this problem;

The acceleration of a marble in a certain fluid is proportional to the speed of the marbles, and is given (in SI units) by a= -3.00V^2 for v>0. If it enters this fluid with a speed of 1.50 m/s, how long will it take for the marble to reach half its intial speed.


I have released that

Vf=Vi + a(t)

.75=1.5+ a(t)
-.15=a(t)


and that A=(Vf-VI)/t

I am stuck after this. Please help me.

 

[dextercioby]

Do you calculus??This problem involves solving a first ODE through separation of variables...

Daniel.

 

[bjon-07]

I am still stock on this problem. I have tryed using separation of variables but it just leads me in a circle.

 

[Doc Al]

$$\frac{dv}{dt} = -3 v^2$$
$$-\frac{1}{3 v^2} dv = dt$$
Integrate!

 

[bjon-07]

I can't beilve I did not see that LOL, its soo easy. Thank you for your help.