# An abrupt slowdown in concentrated traffic 4

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. The figure 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 $v_{s}=25.0 m/s$. 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?

## 4 thoughts on “An abrupt slowdown in concentrated traffic”

• imperiall

awsome solution..lucid & most encoded.the problem belongs to fundamental of physics(halliday,resnick,walker) of difficulty level having got 3dots.l’ve got resolution too much !!! all the best to everyone !!!??

• Thomas M Galarneau

So, just a thought/question, if people are still here.. – If we are trying to teach ourselves to solve problems such as these, what is a good strategy to be self-sufficient one day? Any problem-solving advice/strategy would be greatly appreciated. What is the expectation (time) that we won’t need to seek out solutions in the back of the book or google to solve? Thanks in advance. Merry Christmas

• questionsolutions Post author

This is from my personal experience as a university student. The more questions you do, the better you get at it. In fact, I think at some point, after doing so many questions, the second you see a question, you start to formulate a method to solve it. It becomes a natural instinct. I guess one way to look at is the way we look at simple mathematics. When we first learned the Pythagorean theorem, it wasn’t simple, at least not the first day, but now, it’s almost second nature to us, and that’s simply because we had to solve many questions involving the same type of principles over and over again. Eventually, you also start getting an idea of whether the answer you got is right or wrong. It’s only a matter of how many questions it takes for us to reach that point. This is completely dependent on each of us. Some students gain insight faster than others, but all it means for others is that we just keep trying. Though at first, it seems like these questions can be daunting, they do become much easier as time goes on.

Some simple tips I can say is to make sure you list out what is given in a question. As simple as this seems, it’s incredible how helpful this is. Also, draw a diagram, always draw it out if you can, even if it’s just a simple line drawing. We can think better when we visualize things. Don’t skip the hard questions. Try them, figure out where you went wrong, and then do a similar question until you get it. Eventually, it gets much easier. Lastly, teach what you learn. You’ll find that when you try to teach something, you have to think twice as hard to explain it in simpler terms, and it always leads to you gaining a better understanding of the problem. If you don’t have anyone to teach, pretend to teach yourself, in the simplest way possible. It will do wonders!

Have a very Merry Christmas and a very happy new year! Best of luck with your studies ðŸ™‚