Re: Kinetics and integration

Quote:

Originally Posted by

**Trianagt** The **speed** of a regional airliner during its take off run is a=A-Bv^2. Where v is its **speed** and A and B are positive constants.

Why do you denote speed with two different letters: a and v?

Re: Kinetics and integration

The a stands for the acceleration. I hope that helps!

Re: Kinetics and integration

Since a(t) = dv / dt, we have a differential equation dv / dt = A - Bv^2. It can be solved using separation of variables. This gives v(t) and answers 2. Answering 1 involves finding the inverse of v(t). Answering 3 requires finding $\displaystyle \int_0^t v(u)\,du$ where t is the answer to question 1.

Re: Kinetics and integration

$\displaystyle \frac{1}{A- Bv^2}= \frac{1}{(\sqrt{A}- \sqrt{B}v)(\sqrt{A}+ \sqrt{B}v)}$

Use "partial fractions to separate those and integrate each using the substitution $\displaystyle x= \sqrt{A}- \sqrt{B}v}$ for the first, $\displaystyle y= \sqrt{A}+\sqr{B}v$ for the second.