Integrating to determine speed as a function of time

[AryRezvani]

Homework Statement

Homework Equations

The above formulas

The Attempt at a Solution

I'm lost on where to start with this. The object has an intial velocity in the X direction and has the resistive force of the plontons acting upon it when it lands. What exactly is the equation located in the problem?

 

[tiny-tim]

Hi AryRezvani!

What exactly is the equation located in the problem?

That's good ol' Newton's second law, F = ma

F = -bv, ma = mdv/dt, so mdv/dt = bv, so dv/v = -b/m dt

(the "m =" appears to be a misprint)

 

[AryRezvani]

Hi AryRezvani! That's good ol' Newton's second law, F = ma

F = -bv, ma = mdv/dt, so mdv/dt = bv, so dv/v = -b/m dt

(the "m =" appears to be a misprint)

Thanks for the response Tiny-Tim :)

Okay, so i follow you somewhat. F = -bv (general formula for resistive force).

According to Newton's second law, F=ma which can be rewritten as F=m(dv/dt).

You then equate those two, and you get m(dv/dt)=-bv.

What happens after this? (dv/v) is the derivative of velocity with respect to velocity?

 

[tiny-tim]

(dv/v) is the derivative of velocity with respect to velocity?

ah, no …

∫ dv/v is a short way of writing ∫ (1/v) dv …

just integrate it! ​

 

[AryRezvani]

Ohh so when you integrate that you get ln(v)?

 

[tiny-tim]

Ohh so when you integrate that you get ln(v)?

yes!

(to be precise, ln(v) - ln(v_o))