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8. (a) Define uniform acceleration. What is the acceleration of a body moving with uniform velocity? (b) A particle moves over three quarters of a circle of radius r. What is the magnitude of its displacement?

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Uniform Acceleration Definition: Uniform acceleration refers to a situation where an object's velocity changes at a constant rate over time. In other words, the object's speed increases or decreases by the same amount in each successive equal interval of time. Acceleration of a Body with Uniform Velocity:...
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Uniform Acceleration

Definition: Uniform acceleration refers to a situation where an object's velocity changes at a constant rate over time. In other words, the object's speed increases or decreases by the same amount in each successive equal interval of time.

Acceleration of a Body with Uniform Velocity: When a body is moving with uniform velocity, its acceleration is zero. This means that the object maintains a constant speed and direction, hence no change in velocity, and consequently, no acceleration.

Magnitude of Displacement for a Particle Moving Over Three Quarters of a Circle

Given:

  • Particle moves over three quarters of a circle of radius rr.

Calculation:

  1. Circumference of the Circle:

    • Circumference CC of a circle with radius rr is given by C=2πrC=2πr.
  2. Three Quarters of the Circle:

    • Three quarters of the circumference is 34×2πr43×2πr.
  3. Magnitude of Displacement:

    • The displacement is the shortest distance between the initial and final positions.
    • When a particle moves over three quarters of a circle, its displacement is equal to the diameter of the circle.
    • Diameter DD of the circle with radius rr is given by D=2rD=2r.

Result:

  • The magnitude of the displacement for a particle moving over three quarters of a circle of radius rr is equal to 2r2r.
 
 
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