Answer:
TMS = 45.78 m/s
SMS = 45.66 m/s
Step-by-step explanation:
Vehicle Travel Time (s)
1 40.5
2 44.2
3 41.7
4 47.3
5 46.5
6 41.9
7 43.0
8 47.0
9 42.6
10 43.3
Time mean speed and space mean speed are parameters used to express the speed of a group of vehicles in traffic flow.
Time mean speed is given as the average speed of all the cars
The speed for each vehicle is calculated by dividing the (2000 ft) distance by the time taken by each vehicle to complete that segment of the journey.
Let vehicle = V
Travel time = time
Speed = s
V | Time | speed (ft/s)
1 | 40.5 | 49.383
2 | 44.2 | 45.249
3 | 41.7 | 47.962
4 | 47.3 | 42.283
5 | 46.5 | 43.011
6 | 41.9 | 47.733
7 | 43.0 | 46.512
8 | 47.0 | 42.553
9 | 42.6 | 46.948
10| 43.3 | 46.189
TMS = (Σsᵢ)/N
Σsᵢ = (49.383+45.249+47.962+42.283+43.011+47.733+46.512+42.553+46.948+46.189)
Σsᵢ = 457.823
N = number of vehicles = 10
TMS = 457.823 ÷ 10 = 45.7823 = 45.782 m/s
b) Space mean speed is given as
SMS = N ÷ [Σ (1/sᵢ)]
V | Time | speed | (1/sᵢ)
1 | 40.5 | 49.383 | 0.02025
2 | 44.2 | 45.249 | 0.02210
3 | 41.7 | 47.962 | 0.02085
4 | 47.3 | 42.283 | 0.02365
5 | 46.5 | 43.011 | 0.02325
6 | 41.9 | 47.733 | 0.02095
7 | 43.0 | 46.512 | 0.02150
8 | 47.0 | 42.553 | 0.02350
9 | 42.6 | 46.948 | 0.02130
10| 43.3 | 46.189 | 0.02165
Σ (1/sᵢ) = (0.02025+0.02210+0.02085+0.02365+0.02325+0.02095+0.02150+0.02350+0.02130+0.02165)
Σ (1/sᵢ) = 0.219
SMS = 10 ÷ [Σ (1/sᵢ)] = 10 ÷ 0.219
SMS = 45.662 m/s
Hope this Helps!!!
