Block on Inclined Plane: Velocity & Displacement Eqns & Calcs

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The discussion focuses on a physics problem involving a 64-lb block sliding down a 30-degree inclined plane with a coefficient of friction of 0.25 and a drag force proportional to its velocity. Participants are tasked with determining the equations for the block's velocity and displacement, as well as calculating these values after 5 seconds. The key steps involve identifying the forces acting on the block and setting up the corresponding differential equation using F = ma. The forum emphasizes the importance of correctly expressing forces and acceleration to solve the problem. Overall, the thread aims to guide users through the process of modeling the motion of the block on the inclined plane.
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Problem: A 64-lb block is released from the top of a plane inclined at 30 degrees to the horizontal. As the block slides down the plane, its coefficient of friction is 0.25, and it experiences a drag force due to air resistance equal to one-half is velocity in ft/sec. (a) Determine the equation for the velocity of the block. (b) Determine the equation for the displacement of the block, (c) Calculate the displacement and velocity of the block 5 sec after it is released.
 
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I understand the formulas for the force and everything but I need help setting up the differential equation
 
After you have expressions for each of the forces and for the acceleration, write
F = ma
Then, beneath that, in the corresponding positions, rewrite it using the expressions you found. That will give you the differential equation you have to solve.
 

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