Traffic shock wave. An abrupt shlowdown 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 2-17 shows a uniformly spaced line of cars moving at speed `v=25.0` m/s toward a uniformly spaced line of slow cars moving at speed `v_(s)=5.00` 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 ? It the separation is twice that amount, what are the (b) speed and (c) direction ( upstream or downstream ) of the shock wave ?

Answer

(a) 48.0 m; (b) 2.50 m/s; (c) direction of the shock wave is downstream