Average speed vs average velocity

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SUMMARY

The discussion centers on calculating the average speed and average velocity of a particle based on its displacement at two time intervals. The average velocity is determined to be 0i - 0.25j - 0.125k, while the average speed is calculated to be 0.28 m/s. The average speed is derived from the total distance traveled divided by the time interval, contrasting with average velocity, which is expressed in vector form with three components. This distinction highlights that speed is a scalar quantity, while velocity is a vector quantity.

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  • Understanding of vector mathematics
  • Familiarity with kinematic equations
  • Knowledge of scalar vs. vector quantities
  • Basic calculus for calculating distances
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  • Study the concept of displacement and its relation to distance
  • Learn how to calculate the magnitude of a vector
  • Explore kinematic equations for motion in three dimensions
  • Investigate the differences between average speed and instantaneous speed
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Students in physics, educators teaching kinematics, and anyone seeking to understand the fundamental differences between average speed and average velocity in motion analysis.

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Homework Statement



(a) A particle has a displacement r1 = (35.0i + 12.0j + 14.0k) m at 29.0 s. At 53.0 s the ball has a displacement of r2 = (35.0i + 6.0j + 11.0k) m.

What is the average speed of the ball between 29.0 s and 53.0 s?


The Attempt at a Solution



Having checked the answers, I already know that the average velocity of the ball between 29.0 s and 53.0 s is:

0i-0.25j-0.125k.

The answers suggests that the average speed of the ball is 0.28 m/s. How do I obtain this answer?

I got the average velocity using the formula v_{x, avg} = \frac{\Delta x}{\Delta t} where x is the displacement. I think to find the average speed I must use v_{avg} = \frac{d}{\Delta t} where d is the total distance traveled. But I don't understand why average velocity is in 3 components whereas the average speed is just a single number!
 
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Speed is a scalar quantity. Velocity is a vector, or course.

What is the length of the vector 0\hat{i}-0.25\hat{j}-0.125\hat{k} ?
 

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