Analyzing the Motion of a Particle Under Drag Force

[Demonsthenes]

Homework Statement

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.

Homework Equations

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.

The Attempt at a Solution

Ive tried many different looks at this problem... though nothing is working...

 

[lalbatros]

I have checked A) and B), and these are right.
I did it by solving the equation of motion.
I you have problems to solve the equation of motion, start by checking that indeed A) and B) are solutions, this may help you to see how this can be obtained by solving the equation of motion.
Next time you might not have the solution available for cheating!

 

[PhanthomJay]

Homework Statement

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.

Homework Equations

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.

The Attempt at a Solution

Ive tried many different looks at this problem... though nothing is working...

Have you attempted to apply Newton's 2nd law? Note that the force is variable, and hence the acceleration is noit constant. Are you good in solving differential equations? I also note that your force equation is wrong...F = -bv^2 if F is proportional to the square of the speed...