Average speed vs average velocity

AI Thread Summary
The discussion centers on calculating the average speed and average velocity of a particle over a specified time interval. The average velocity is given as a vector with components 0i - 0.25j - 0.125k, while the average speed is determined to be 0.28 m/s. The participant understands that average speed is a scalar quantity derived from total distance traveled divided by time, contrasting with average velocity, which includes directional components. There is confusion regarding the relationship between the vector components of average velocity and the scalar nature of average speed. The thread seeks clarification on how to calculate the length of the velocity vector and its relevance to determining average speed.
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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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