Question

Consider three vehicles running on a circular track of circumference 2 km. Vehicle A travels at a constant speed of 30 km/h, vehicle B travels at 60 km/h and vehicle C travels at 90 km/hr. Calculate the ratio of space mean speed over time mean speed.

Answer 1

Space mean speed is defined as the average of speed measurements at a particular instant of time of all vehicles over a particular instant of time of all vehicles over a particular stretch of highway.

The formula for Space mean speed is,

Where,

D is the length of road considered

ti is the time taken by the ith vehicle to cross the considered road length.

n is the number of vehicles observed

Here, n = 3

D = 2 km

V1 = 30 km/hr

V2 = 60 km/hr

V2 = 90 km/hr

Therefore the equation for space mean speed becomes,

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Time mean speed is defined as the average of the speed measurements at one point in space of all vehicles passing over a period of time.

The equation for Time mean speed is,

Vi = Velocity of ith vehicle

n = number of vehicles

Here, n = 3

V1 = 30 km/hr

V2 = 60 km/hr

V2 = 90 km/hr

So the equation becomes,

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The ratio of space mean speed over time mean speed is,