Average velocity vector of non-uniform circular motion?

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SUMMARY

The discussion focuses on calculating the average velocity vector and average acceleration vector for a particle undergoing non-uniform circular motion. At t=2.0 seconds, the particle, which starts from rest, has completed a quarter revolution with a speed of \(\frac{\pi}{2}\) m/s. The average velocity vector and average acceleration vector require understanding of both tangential and radial acceleration components, calculated using the equations \(a_{tan} = \frac{dv}{dt}\) and \(a_R = \frac{v^2}{r}\). The participant emphasizes the need for clarity in vector calculations and the importance of including units in the final answers.

PREREQUISITES
  • Understanding of circular motion dynamics
  • Familiarity with vector mathematics
  • Knowledge of kinematic equations (SUVAT equations)
  • Basic calculus for differentiation
NEXT STEPS
  • Study the derivation and application of SUVAT equations in circular motion
  • Learn about vector representation in physics, particularly in circular motion
  • Explore the relationship between tangential and radial acceleration
  • Practice problems involving average velocity and acceleration in non-uniform circular motion
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Students studying physics, particularly those focusing on mechanics and circular motion, as well as educators looking for examples of non-uniform circular motion problems.

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Homework Statement


A particle starting from rest revolves with uniformly increasing speed in a clockwise circle in an xy plane. The center of the circle is at the origin of an xy coordinate system. At t=0, the particle is at x=0.0m, y=2.0m. At t=2.0s, it has made one-quarter of a revolution and is at x=2.0m,y=0.0m.

(a) Speed at t=2.0s?
(b) Average velocity vector?
(c) Average acceleration vector during this interval.

Homework Equations



$$a_{tan} = \frac{dv}{dt}$$
$$a_R = \frac{v^2}{r}$$
$$a = \sqrt{a^2_{tan}+a^2_{R}}$$

The Attempt at a Solution



a)
$$r = 2$$
$$d = \frac{2 \pi (2)}{4} = \pi$$
$$v = \frac{\pi}{2}$$

b, c) I don't know where to start because it's asking for a vector which implies that we need to calculate the "average angle" ?
 
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Your answer for a) is wrong. what equations do you know for uniform acceleration? (Usually called the SUVAT equations.)
Also, you should state the units in the answers.
 

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