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=-3.00 v^2 for v greater than 0. If the marble enters this fluid with a speed of 1.20 m/s, how long will it take before the marble's speed is reduced to half of its initial value?
Another way of writing a is dv/dt. So we have the equation:
dv/dt = -3*v^2
Divide both sides by v^2 and multiply ...
The solution is given in an equation with short descriptions explaining how to do it.