Jam Shock Speed
On a highway, there are 100 cars per kilometer and the cars are all moving at . One car notices something and slams on its breaks, slowing down to and halving the distance between itself and the car behind it.
How quickly does the shock wave generated move relative to the ground (in )?
Give your answer to 3 decimal places.
The answer is 0.
This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try
refreshing the page, (b) enabling javascript if it is disabled on your browser and,
finally, (c)
loading the
non-javascript version of this page
. We're sorry about the hassle.
The velocity v L before the shock is 100 km/hr, and the velocity v R after the shock is 50 km/hr. The density after the shock is twice the density before the shock (since the distance between cars is halved) so k R = 2 0 0 cars/km and k L = 1 0 0 cars/km.
v w = k R − k L q R − q L v w = 2 0 0 − 1 0 0 ( 2 0 0 ∗ 5 0 ) − ( 1 0 0 ∗ 1 0 0 ) = 0
Note: relative to the ground, the shock moves at 0 km/hr. But for all the cars moving at 100 km/hr, that means that the shock is coming towards them at 100 km/hr.