Ten particles are moving at the speed of `2,3,4,5,5,5,6,6,7 and 9ms^(-1)`. Calculate rms speed, average speed and most probable speed.

Explanation

The average speed
`overline(v)=(2+3+4+5+5+5+6+6+7+9)/(10)=5.2ms^(-1)`
To find the rms speed, first calculate the mean square speed `overline(v_(2))`.
`overline(v_(2))=(2^(2)+3^(2)+4^(2)+5^(2)+5^(2)+5^(2)+6^(2)+6^(2)+6^(2)+7^(2)+9^(2))/(10)`
`=30.6m^(2)s^(-2)`
The rms speed
`v_(rms)=sqrt(overline(v^(2)))=sqrt(30.6)=5.53ms^(-1)`
The most probable speed is `5ms^(-1)` because three of the particles have that speed.