Equation of Motion of a Particle acted on by a retarding force

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SUMMARY

The discussion centers on the equation of motion for a particle subjected to a retarding force. Participants seek clarification on the mathematical expression involved, specifically regarding the correct placement of brackets and the nature of variables such as "a" and "y". It is established that "a" represents a constant acceleration, while "y" is defined as a function of time "t". The conversation emphasizes the importance of correctly interpreting these variables to solve the motion equation accurately.

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  • Understanding of classical mechanics principles
  • Familiarity with differential equations
  • Knowledge of variable functions in physics
  • Basic algebraic manipulation skills
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  • Study the principles of Newton's laws of motion
  • Learn about retarding forces and their impact on motion
  • Explore the concept of functions and their derivatives in physics
  • Investigate the mathematical techniques for solving differential equations
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Students of physics, educators teaching mechanics, and anyone interested in understanding the dynamics of motion under retarding forces.

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Homework Statement
The equation of motion is $$\frac{d^2r}{dt^2} = a - y\frac{dr}{dt}$$
At time t = 0, $$r = r_0$$ and $$\frac{dr}{dt} = v_0$$
Show that $$d[a \times (yr + dr/dt]/dt = 0$$
and find the differential equation satisifed by $$s = a.r$$
Relevant Equations
Unsure
I really can't figure out where to even start on this question
 
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Can you fix the brackets in the expression you are to show is 0? Also, is "a" a constant? And is y a function of t?
 

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