Question

From consecutive aerial photos of traffic along a highway, one observes that there are ten cars per kilometer with 0 velocity (they are parked), forty cars per kilometer traveling at 15 km/hr and twenty cars per kilometer traveling at 30 km/hr. Determine the space mean speed of traffic and the time mean speed

Answer 1

The space mean speed is
`V_s = \ 18Km/hr`

The Time mean speed is
`V_t= 20 km/hr`

Step-by-step explanation:

From the question we can derive that

Velocity (Km / h)(V) 0(
`V_1`) 15(
`V_2`) 30(
`V_3`)

No of Cars(N) 10(
`N_1`) 40 (
`N_2`) 20(
`N_3`)

From the table above the space mean speed would be

`V_s = (N_2 + N_3)/((N_2)/(V_2) + (N_3)/(V_3) )`

`V_s = (40 +20 )/((40)/(15) + (20)/(30) )`

`V_s = \ 18Km/hr`

From the table above the Time mean speed would be

`V_t = ((N_2 * V_2 ) + (N_3 * V_3 ))/(N_2 +N_3)`

`V_t = ((40* 15 )(30*20))/(40+ 20)`

`= 20 km/hr`

We did not make use of
`N_1` because the speed was zero