Solar Racer in trouble.

We are in the annual solar race in Australia and have gone 500 Km but its been cloudy so the poor solar powered racer can only manage 50 KM/hr for the first 500 Km. Then at that point, the clouds go away and the little racer can get to its top speed of 80 Km/hr. Assuming no accel time, just a jump function to make it simpler, how many Km/hr per km does the total average go up? For instance, one klick past the 500 klick mark the car has just done that one click at 80, how much has the average for the 501 Klicks gone up, then the next klick, etc. Is this a linear curve? Power curve? What is the function of the change in average velocity say summing it up for the next 500 Km where the vehicle goes 80 klicks the whole second part.

Here's the graph if the race is 5000km long. The shape after 1000km total isn't very interesting.

http://img237.imageshack.us/img237/7544/averageni5.jpg

Originally posted by XanthosNZ
Here's the graph if the race is 5000km long. The shape after 1000km total isn't very interesting.

http://img237.imageshack.us/img237/7544/averageni5.jpg

except it asymtotically approaches 80.
BTW, the graph has some interesting dithering effects in it when viewed on my notebook, you see it when you tilt the screen. Is that a deliberate effect or just how that curve comes out?

Originally posted by sonhouse
except it asymtotically approaches 80.
BTW, the graph has some interesting dithering effects in it when viewed on my notebook, you see it when you tilt the screen. Is that a deliberate effect or just how that curve comes out?

I thought the asymptote would be obvious to anyone with a brain. I mean really.
And yes I put extra things into the picture just to mess with you.

Originally posted by XanthosNZ
I thought the asymptote would be obvious to anyone with a brain. I mean really.

Still without social skills?

Originally posted by FabianFnas
Still without social skills?

🙄

Breaking News: A car can never reach an overall average speed of 80km/hr by travelling at 80km/hr if it at any previous point averaged less than 80km/hr.

Originally posted by FabianFnas
Still without social skills?

The shape is hardly interesting for the first 1000 km. This is not some radically challenging curve with deep meaning and the tendencies are obvious. XNZ showed excellent social skills by not giving every bit of information. Occasionally it is nice to assume that the reader of the text is not brain dead.

EDIT: By that I mean that the reader can extrapolate their own information.
EDIT: By that I mean that the reader can read the information given and make some conclusions on their own. Especially if they are obvious.

Originally posted by XanthosNZ
🙄

Breaking News: A car can never reach an overall average speed of 80km/hr by travelling at 80km/hr if it at any previous point averaged less than 80km/hr.

I didn't need the graph to see that, I knew it up front, just pointed it out thats all.