General Physics 1st Semeste Problem 1. Traffic shock wave An abrupt slowdown in

Question

General Physics 1st Semeste Problem 1. 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 1 shows a uniformly spaced line of cars moving at speed25.0 m/s toward a uniformly spaced line of slow cans moving at speed v,-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? If the separation is twice that amount, what are the (b) speed and (c) direction (upstream or downstream) of the shock wave? L. Car Buffer

Explanation / Answer

Given,

v = 25 m/s ; vs = 5 m/s ; L = 12 m ;

a)We know that, v = D/t => D = vt

t = L/vs = 12/5 = 2.4 s

D = 25 x 2.4 = 60 m

d = D - L = 60 - 12 = 48 m

Hence, d = 48 m

b)intial separation:

d' = 2 x 48 = 96 m

t = (d' + x)/v = x/vs

x = vs d'/(v - vs)

x = 5 x 96/(25 - 5) = 24 m

t = 24/5 = 4.8 s

X = 24 - 12 = 12 m

v(shock) = 12/4.8 = 2.5 m/s

Hence, V(shock) = 2.5 m/s

c)Direction will be downstream

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