How Do Traffic Signal Timings Affect Car Speed Calculations?

[brad sue]

Hi,
this is a problem I have . But because I cannot include the graph, I try to do via Microsoft Word. I put it as an attachment. I hope that you will understand it.

This is the problem:

Traffic signals are placed along a straight road at positions x = 0 m, x = 600 m, and x = 1200 m (see graph in attachment)). The time intervals during which the signals are green are shown by the thick lines ( in red) in the figure.

(a) Draw the displacement-versus-time curves (fastest and slowest) for a car that passes through all the lights when the car moves with constant speed.

(b) Draw a similar set of lines for a car traveling in the opposite direction.

(c) Assuming that the lights are timed such that a car passes through all lights in the middle of the time interval, what is the speed for which the lights are timed?

(d) What is the fastest constant speed of a car that makes it through all the signals, assuming it arrives at the first light at the optimal moment?

For info.:
The grah is a 2 dimension space with time(s) on horizontal and the position x(m) in vertical.
The interval are put in red and I mentioned the time interval at the end of each line.Please help me with that . I do not understand it

Thank you very much.

Brad

 

[Astronuc]

Well if you map x=x(t), then v = dx/dt and the slope is speed (or magnitude of velocity).

If you draw a straight line, it's slope will be a constant speed.

So the fastest speed, will have the steepest slope.

 

[brad sue]

ok!

Thank you that make more sense now , but what about quesion c

I do not understand this question .
Thanks

Brad

Well if you map x=x(t), then v = dx/dt and the slope is speed (or magnitude of velocity).

If you draw a straight line, it's slope will be a constant speed.

So the fastest speed, will have the steepest slope.