Question

The speeds of 22 particles are as follows: two at 5.30 cm/s, four at 1.40 cm/s, six at 7.14 cm/s, eight at 1.52 cm/s, two at 7.68 cm/s. What are (a) vavg, (b) vrms, and (c) vP?

Answer 1

Average velocity is 3.93 cm/s

Root mean square velocity is 4.79 cm/s

Velocity peak to peak is 6.28 cm/s

Step-by-step explanation:

Speed of 2 particles = 5.3 cm/s

Speed of 4 particles = 1.4 cm/s

Speed of 6 particles = 7.14 cm/s

Speed of 8 particles = 1.52 cm/s

Speed of 2 particles = 7.68 cm/s

`v_(avg)=(2* 5.3+4* 1.4+6* 7.14+8* 1.52+2* 7.68)/(22)\\\Rightarrow v_(avg)=(86.56)/(22)\\\Rightarrow v_(avg)=3.93\ cm/s`

Average velocity is 3.93 cm/s

`v_(rms)=\sqrt{(2* 5.3^2+4* 1.4^2+6* 7.14^2+8* 1.52^2+2* 7.68^2)/(22)}\\\Rightarrow v_(rms)=\sqrt{(507.34)/(22)}\\\Rightarrow v_(rms)=4.79\ cm/s`

Root mean square velocity is 4.79 cm/s

`v_p=7.68-1.4=6.28\ cm/s`

Velocity peak to peak is 6.28 cm/s