Question

Fifteen identical particles have various speeds: one has a speed of 2.00 m/s, two have speeds of 3.00 m/s, three have speeds of 5.00 m/s, four have speeds of 8.00 m/s, three have speeds of 9.00 m/s, and two have speeds of 15.0 m/s. Find:
a. the average speed
b. the rms speed
c. the most probable speed of these particles.

Answer 1

Answer:

a)  $V=7.5m/s$

b) $rms=8.4m/s$

c) Generally the most probable speed is 8m/s as it the most posses by particles being the average

Explanation:

From the question we are told that:

Sample size N=15

  $Speed 1 v_1=2m/s\\\\Speed 2 v_2=3m/s\\\\Speed 3 v_2=5m/s\\\\Speed 4 v_4=8m/s\\\\Speed 3 v_5=9m/s\\\\Speed 2 v_6=15m/s$

Generally the equation for Average speed is mathematically given by

 $V_{avg}=\frac{\sum(nv)}{N}$

Therefore

 $V_{avg}=\frac{(2+2(3)+3(5)+4(8)+3(9)+2(15))}{15}$

 $V=7.5m/s$

b)

Generally the equation for RMS speed of the particle is mathematically given by

  $rms=\sqrt{\frac{\sum(nv^2)}{N}}$

  $rms=\sqrt{\frac{2^2+2(3)^2+3(5)^2+4(8)^2+3(9)^2+2(15)^2}{15}}$

  $rms=\sqrt{69.73}$

  $rms=8.4m/s$

c

Generally the most probable speed is 8m/s as it the most posses by particles being the average