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Assume you are an observer standing at a point along a three-lane roadway. All vehicles in lane 1 are traveling at 30 mi/h, all vehicles in lane 2 are traveling at 45 mi/h, and all vehicles in lane 3 are traveling at 60 mi/h. There is also a constant spacing of 0.5 mile between vehicles.
If you collect spot speed data for all vehicles as they cross your observation point, for 30 minutes,
what will be the time- mean speed and space-mean speed for this traffic stream?

Respuesta :

Answer:

Explanation:

Given data;

  • In line 1, v1 = 30mi/hr
  • in line 2, v2 = 45mi/hr
  • in line 3, v3 = 60mi/hr
  • therefore time mean speed = v1 + v2 + v3 /n
  • = VT = 45mi/hr

  • space mean speed ; Vs
  • harmonic mean = 1/V = 1/v1 + 1/v2 + 1/v3
  • V = 13.85mi/hr
  • Hence Vs = V x n = 3 x 13.85 = 41.55mi/hr
Cricetus

The time mean speed is "45 mi/hr" and space mean speed is "41.55 mi/hr".

Given:

In line 1, 2 and 3,

  • [tex]V_1 = 30 \ mi/hr[/tex]
  • [tex]V_2 = 45 \ min/hr[/tex]
  • [tex]V_3 = 60 \ mi/hr[/tex]

→ The time mean speed will be:

= [tex]\frac{V_1+V_2+V_3}{n}[/tex]

= [tex]\frac{30+45+60}{3}[/tex]

= [tex]\frac{135}{3}[/tex]

= [tex]45 \ mi/hr[/tex]

Now,

The harmonic mean will be:

= [tex]\frac{1}{V}[/tex]

= [tex]\frac{1}{V_1} +\frac{1}{V_2} +\frac{1}{V_3}[/tex]

= [tex]13.85 \ mi/hr[/tex]

hence,

The space mean speed will be:

= [tex]V\times n[/tex]

= [tex]3\times 13.85[/tex]

= [tex]41.55 \ mi/hr[/tex]

Thus the above answer is correct.

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