Differential Equation and Newtons 2. law

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In a fluid, the exponential force opposing movement is given by F = -b*e^v, where b is a constant and v is the object's velocity. To derive a differential equation for an object of mass m using Newton's second law (F = ma), the resistive force must be equated to the mass times acceleration. This leads to a separable differential equation where velocity v is isolated on one side and time t on the other. The discussion emphasizes the need to express the equation in terms of velocity. The final goal is to solve for v as a function of time.
Atilla1982
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In a fluid, there's an exponential force F = -b*e^v working against the direction of movement. B is constant, and v is the objects velocity in m/s.

They want me to use Newtons 2. law to find a differential equation for the movement of an object with mass m. The equation is separable, separate so v is found on one side of the = and t on the other side.

Could anyone please point me in the right direction here?
 
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Atilla1982 said:
In a fluid, there's an exponential force F = -b*e^v working against the direction of movement. B is constant, and v is the objects velocity in m/s.

They want me to use Newtons 2. law to find a differential equation for the movement of an object with mass m. The equation is separable, separate so v is found on one side of the = and t on the other side.

Could anyone please point me in the right direction here?

what's F = ma in terms of a differential equation?

(i take it that we want it in terms of velocity.)

after you get that step, you equate it to that resistive force, and ... there you go.
 

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