Understanding Acceleration: How a Speed Skater Slows Down on Rough Ice

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A speed skater initially traveling at 8 m/s slows down to 6 m/s after crossing a 5 m wide patch of rough ice. The discussion focuses on calculating her acceleration during this deceleration phase. The skater experiences a steady decrease in speed due to the rough surface. The problem was initially posed for assistance but was later resolved by the user. Understanding the physics of acceleration in this context is crucial for similar scenarios.
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Acceleration.. Need Help !

A speed skater moving across frictionless ice at 8 m/s hits a 5 m wide patch of rough ice. She slows steadily, then continues on at 6m/s. What is her acceleration on the rough ice?

Please help. I don't know how to solve this.
 
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nevermind. i figured it out.
 
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 .
TL;DR Summary: I came across this question from a Sri Lankan A-level textbook. Question - An ice cube with a length of 10 cm is immersed in water at 0 °C. An observer observes the ice cube from the water, and it seems to be 7.75 cm long. If the refractive index of water is 4/3, find the height of the ice cube immersed in the water. I could not understand how the apparent height of the ice cube in the water depends on the height of the ice cube immersed in the water. Does anyone have an...
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