Five molecules have speeds of 12 ,16,32,40, and 48 m/s find (a) the average speed `v_(avg ) ` and (b) the rootmean - square speed ` v_(rms) ` for these molecules (c ) show that for any distribution of speeds `, v_(rms ) ge V_(avg)`

Explanation

To solve the problem, we will calculate the average speed \( v_{\text{avg}} \) and the root-mean-square speed \( v_{\text{rms}} \) for the five molecules with speeds of 12 m/s, 16 m/s, 32 m/s, 40 m/s, and 48 m/s. Finally, we will show that \( v_{\text{rms}} \geq v_{\text{avg}} \).

### Step 1: Calculate the Average Speed \( v_{\text{avg}} \)

The average speed is calculated using the formula:

\[
v_{\text{avg}} = \frac{v_1 + v_2 + v_3 + v_4 + v_5}{n}
...