Traffic shock wave. An abrupt slowdown in concentrated traffic can travel as a p

Question

Traffic shock wave. An abrupt slowdown in concentrated traffic can travel as a pulse, termed a shock wave, along the line of cars, either downstream (in the traffic direction) or upstream, or it can be stationary. Figure 2-22 shows a uniformly spaced line of cars moving at speed v = 29.0 m/s toward a uniformly spaced line of slow cars moving at speed vs = 5.20 m/s. Assume that each faster car adds length L = 12.0 m (car length plus buffer zone) to the line of slow cars when it joins the line, and assume it slows abruptly at the last instant. (a) For what separation distance d between the faster cars does the shock wave remain stationary? If the separation is twice that amount, what are the (b) speed and (c) direction (upstream denote 1 and downstream denote 0) of the shock wave?

Explanation / Answer

ince the slow zone is moving at 5m/s, if the shock front is to remain stationary, then there must be 5m/s of cars being added to it. Each car will add 12m to the length of the slow zone, so a car must join the slow zone once every 2.4 seconds (12/5). Given that time separation, and the speed of 25m/s for the fast zone, the cars must be separated by 60m (25*2.4). If the cars are separated by twice this distance, then 12m get added to the end of the shock zone every 4.8s (120/25). So that comes out to 2.5m/s (12/4.8). Thus the shockwave advances down the roadway at 2.5m/s (5-2.5),

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