Proving Constant Horizontal Velocity for Particle w/ Drag Force

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A particle of mass m traveling at a constant horizontal velocity v0i experiences a drag force proportional to the square of its speed, represented as Fd = -b/v^2i. To prove the particle's speed as a function of position, v(x) = v0 e^(-bx/m), one must apply differential equations to the drag force. The acceleration can be derived as a(x) = -(b/m)v0^2 e^(-2bx/m) by relating force to acceleration and solving the resulting equations. This discussion emphasizes the mathematical relationship between drag force, velocity, and acceleration in a particle's motion. The analysis provides a clear understanding of how drag affects a particle's speed and acceleration over time.
Demonsthenes
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Prove this...

A particle of mass m is traveling along the x-axis with a constant horizontal velocity v0i. When the particle passes through the origin, it experiences a Drag Force which is proportional to the square of the particle's speed (Fd = - b/v^2i... drag coefficient b.

Questions

A) Show that the particle's speed is then given by v(x) = v0 e^-bx/m.

B) Show that the particle's acceleration is then given by a(x) = -(b/m)v0^2 e^-2bx/m.
 
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try differential equation. You have the force , therefore can find the acceleration with respect to the velocity. solve the dif eq and find the velocity.
 

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