Well, the problem says:(adsbygoogle = window.adsbygoogle || []).push({});

From some height a objectwith mass mis thrown . Determinate the law that describes how the velocity of fall v changes, if on the object, besides gravity, acts the force air resistance, which is proportional to velocity v (the proportionality coefficient is k), ie must be found v= f(t)

Then, by the second Newton's law, we have.

$$m\cdot\frac{dv}{dt}=mg-kv$$

AND THEN, HERE'S WHAT I DON'T UNDERSTAND. My textbook says:

Is easy to proof that every function:

$$v=Ce^{-\frac{k}{m}t}+\frac{mg}{k}$$

Satisfies the first equation.

Can somebody explain me in detail, why is that true? Thanks.

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# I Help with basic problem of kinematics

Have something to add?

Draft saved
Draft deleted

Loading...

Similar Threads for Help basic problem |
---|

A Stefan Problem |

A Solving an ODE Eigenvalue Problem via the Ritz method |

I Need a help in solving an equation (probably differentiation |

A Understanding dummy variable in solution of 1D heat equation |

**Physics Forums | Science Articles, Homework Help, Discussion**