Question

Spot speeds of vehicles observed at a point on a highway are 40, 55, 60, 65 and 80 km/h. The space - mean speed (in km/h, round off to two decimal places) of the observed vehicles is ______.

Answer 1

Concept: 

Space mean speed(V_s): 

The space-mean speed is the average speed of vehicles traveling a given segment of the roadway during a specified period of time and is calculated using the average travel time and length for the roadway segment.

 \(V_{s}=\frac{n}{\sum_{i=1}^{\eta }\frac{1}{V_{i}}}\),

Where n = Number of individual vehicles observation. V_i= spot speed of individual vehicles.

Calculation:

Given, 

Four spot speeds given, i.e 40, 55, 60, 65, 80 km/h

n = 5

\(V_{s}=\frac{5}{\frac{1}{V_{1}}+\frac{1}{V_{2}}+\frac{1}{V_{3}}+\frac{1}{V_{4}}+\frac{1}{V_{5}}}\)

\(V_{s}=\frac{5}{\frac{1}{40}+\frac{1}{55}+\frac{1}{60}+\frac{1}{65}+\frac{1}{80}}\) = 56.99 kmph