# Average speed vs average velocity

## 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!

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