The molecules of a five-particle gas have these velocities: 3.0i + 4.0j, - 2.0i + j, - 5.0j, i - 2.0j, and -2.0i + 2.0j. The average speed of the gas is

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The average speed of a gas is calculated by finding the magnitude of each velocity vector (which gives the speed of each particle), summing these speeds, and then dividing by the total number of particles. For the given velocities:1. $ \sqrt{(3.0)^2 + (4.0)^2} = 5.0 $ m/s2. $ \sqrt{(-2.0)^2 + (1.0)^2} = \sqrt{4 + 1} = \sqrt{5} $ m/s3. $ \sqrt{(-5.0)^2} = 5.0 $ m/s4. $ \sqrt{(1.0)^2 + (-2.0)^2} = \sqrt{1 + 4} = \sqrt{5} $ m/s5. $ \sqrt{(-2.0)^2 + (2.0)^2} = \sqrt{4 + 4} = \sqrt{8} $ m/sSumming these speeds: $5.0 + \sqrt{5} + 5.0 + \sqrt{5} + \sqrt{8} = 10 + 2\sqrt{5} + \sqrt{8}$Given $\sqrt{5} \approx 2.24$ and $\sqrt{8} \approx 2.83$, the sum is approximately $10 + 4.48 + 2.83 = 17.31$ m/s.Dividing by the total number of particles (5) gives the average speed: $ \frac{17.31}{5} \approx 3.46 $ m/s.

The Molecules of a Five-Particle Gas Have These Velocities: 3