Can anyone help me solve the differential eqn dv/dt= -8v^2? I have done this repeatedly, and none of my answers work

Question

anonymous · Answer

What do you need to solve?

anonymous · Answer

My question asks, Find the velocity function v(t) if at time t=0, the body is traveling at 94 m/s

anonymous · Answer

I started out by separating the variables, and getting v = 1/(8t+C), where C is a constant. Is this integration wrong?

anonymous · Answer

dv/dt = -8v^2

Integral will be -8v^2t + c.

anonymous · Answer

Since v(t) = 94 when t = 0. In that integral, c = 94.
So, the function is:
v(t) = -8v^2t + 94

anonymous · Answer

Can you walk me through the integration? If I know what I a getting wrong here, I might be able to fix my problems with my other homework numbers. Was my approach to separate variables valid?

anonymous · Answer

It is actually a simple integration. Since the integral is with respect to "t", treat -8v^2 as a constant. Integral of (a * dt) will be "a * t + c". So, you get what I showed.

anonymous · Answer

That is what I forgot...wow...thanks so much for your help!

anonymous · Answer

Very good! No worries.