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

Answer:

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

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

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

                                    $V_s = \frac{N_2 + N_3}{\frac{N_2}{V_2} + \frac{N_3}{V_3} }$

                                    $V_s = \frac{40 +20 }{\frac{40}{15} + \frac{20}{30} }$

                                   $V_s = \ 18Km/hr$

  From the table above the Time mean speed would be

                                 $V_t = \frac{(N_2 * V_2 ) + (N_3 * V_3 )}{N_2 +N_3}$

                                 $V_t = \frac{(40* 15 )(30*20)}{40+ 20}$

                                         $= 20 km/hr$

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