Rating speeds from least to greatest from a position time graph

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The ranking of speeds from least to greatest based on the position-time graph is R > P > Q = S. R has a steeper slope than P, indicating a greater speed. P has a positive slope, confirming it has a non-zero speed. Both Q and S have horizontal slopes, indicating no movement and therefore zero speed. The explanations provided for the rankings are accurate.
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Homework Statement
(E) Rank the values of the particles speed at points P, Q, R, S from fastest to slowest
Relevant Equations
Speed = distance/time
My answer is R > P > Q = S

Since R is more steeper than P the speed is greater, speed is a non-negative unit so i assume that speed of R will be greater than P
Speed of P has a positive slope, also the magnitude is positive.
Q and S are the same due to the fast that they both horizontal slopes which means the object is not moving which means no speed.

This is my work , correct me if i'm wrong, thanks ^^^
1706021404345.png
 
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Ranking and explanations look good.
 
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Thread 'Chain falling out of a horizontal tube onto a table'

Thread 'Chain falling out of a horizontal tube onto a table'

My attempt: Initial total M.E = PE of hanging part + PE of part of chain in the tube. I've considered the table as to be at zero of PE. PE of hanging part = ##\frac{1}{2} \frac{m}{l}gh^{2}##. PE of part in the tube = ##\frac{m}{l}(l - h)gh##. Final ME = ##\frac{1}{2}\frac{m}{l}gh^{2}## + ##\frac{1}{2}\frac{m}{l}hv^{2}##. Since Initial ME = Final ME. Therefore, ##\frac{1}{2}\frac{m}{l}hv^{2}## = ##\frac{m}{l}(l-h)gh##. Solving this gives: ## v = \sqrt{2g(l-h)}##. But the answer in the book...
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