Find the radius of a particle's circular path

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SUMMARY

The discussion focuses on calculating the radius of a particle's circular path using its acceleration vectors at two different times. At t1=3.00s, the acceleration vector is (3i-5j) m/s², and at t2=7.00s, it is (-3i+5j) m/s². The key equation used is the centripetal acceleration formula, defined as centripetal acceleration = v²/r. The relationship between the two acceleration vectors provides insight into the particle's velocity and radius.

PREREQUISITES
  • Understanding of centripetal acceleration
  • Familiarity with vector components in physics
  • Knowledge of circular motion principles
  • Basic algebra for solving equations
NEXT STEPS
  • Study the derivation of centripetal acceleration formulas
  • Learn how to analyze vector components in physics
  • Explore the relationship between velocity and radius in circular motion
  • Practice problems involving acceleration vectors and circular paths
USEFUL FOR

Students studying physics, particularly those focusing on mechanics and circular motion, as well as educators looking for examples of vector analysis in motion problems.

David Williams
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Homework Statement


A particle moves along a circular path over a horizontal xy plane at a constant speed. At time t1= 3.00s, its acceleration vector is given by (3i-5j) m/s^2. At time t2=7.00 s, its acceleration is given by (-3i+5j) m/s^2.
Find the radius of the particle's circular path.

Homework Equations


centripetal acceleration = v^2/r

The Attempt at a Solution


Stumbling around for about an hour with no clue what to do... left me with nothing to show for.
 
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Hello David, :welcome:

David Williams said:
no clue what to do
Doesn't count as an attempt at solution; according to the PF rules we're not allowed to assist in such a case.

But for a first post I'll stick out my neck :rolleyes:: You have two acceleration vectors; notice anything particular about them ? Could that help you towards another expression involving ##v## and ##r## ?
 

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