What is the acceleration and time for a block on an inclined plane?

AI Thread Summary
The discussion centers on calculating the acceleration and time for a block sliding down an inclined plane. The user attempts to apply Newton's second law and kinematic equations but struggles with the correct interpretation of the problem, particularly regarding the block's initial velocity and distance. They calculate forces acting on the block, resulting in an acceleration of 1.5 m/s² down the plane. However, confusion arises over the distance traveled and the initial conditions given in the problem. Clarification on these points is needed to accurately determine the time it takes for the block to slide down the incline.
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I am stuck on a problem from the 5 Steps to a 5: AP Physics B&C book and would really appreciate anyone's help.

Homework Statement


Determine (a) the acceleration of the block down the plane and (b) the time for the block to slide to the bottom of the plane.

http://02.edu-cdn.com/files/static/mcgrawhillprof/9780071623209/INCLINED_PLANES_08.GIF

Homework Equations


F=ma
F, gravity = mg
F, friction = umg
Kinematic equation ?

The Attempt at a Solution



Fx, up the plane = mgsin25 + umgcos25 = 204 N
a = F/m = 204/30 = 6.8 m/s^2
Fx, down the plane = mgsin25 - umgcos25 = 44 N
a = F/m = 44/30 = 1.5 m/s^2

I tried using x = Vot + 1/2 at^2 (x = 20 m, Vo = 3m/s) and v = Vo + at (v = 0, Vo = 3 m/s) to solve for time, but my answers were way off on both attempts.
 
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If the question says the mass is going 3 m/s up the plane, and the a) part asks for the acceleration DOWN the plane this means that x != 20, but it is going to be 20 added to the distance traveled by the mass until it changes direction. I hope that helped.
 
Kindly see the attached pdf. My attempt to solve it, is in it. I'm wondering if my solution is right. My idea is this: At any point of time, the ball may be assumed to be at an incline which is at an angle of θ(kindly see both the pics in the pdf file). The value of θ will continuously change and so will the value of friction. I'm not able to figure out, why my solution is wrong, if it is wrong .
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