Derivative: position, velocity, acceleration as functions of time?

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The discussion revolves around finding the position, velocity, and acceleration of a 1.00 kg glider attached to a spring with a force constant of 25.0 N/m as functions of time. The glider starts at the equilibrium position with an initial velocity of -0.150 m/s, indicating it is moving towards spring compression. Participants are encouraged to consider the initial phase and relevant equations to solve the problem. The request for hints suggests a need for guidance on how to approach the calculations. Overall, the focus is on understanding the relationships between these physical quantities in the context of harmonic motion.
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Derivative: position, velocity, acceleration as functions of time?

Homework Statement



A 1.00 kg glider attached to a spring with a force constant of 25.0 N/m oscillates on a frictionless, horizontal air track. At t = 0, the glider is passing through its equilibrium position with a velocity vx = - 0.150 m/s. (The negative sign means that the glider is headed in the direction which will compress the spring.)

Find the position, velocity, and acceleration as functions of time. Include units. Think carefully about the initial phase.


Homework Equations





The Attempt at a Solution



I am really stuck here. I am not sure how to get started with this question. Thanks for any hints or help anyone can provide.
 
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provide relevant eqns and draw a picture sometimes that helps.
 
Question: A clock's minute hand has length 4 and its hour hand has length 3. What is the distance between the tips at the moment when it is increasing most rapidly?(Putnam Exam Question) Answer: Making assumption that both the hands moves at constant angular velocities, the answer is ## \sqrt{7} .## But don't you think this assumption is somewhat doubtful and wrong?

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