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Cars are faster by race end

Why are cars faster by the end of races with other things being equal?
For example, 60 laps race.
I have 4 stints with 15 laps each stint.
Same hard tyres and fuel levels every stint.
Temperature is the same through all the race.
But I see that every next stint car is faster.
The last stint lap can be faster than first stint lap (same from the start of stint) by 2 seconds actually.
Why is that happening?

The track rubbers in and gets more grip as the race goes on

Is it depends on the tyre type?
Say, I drive on hards 2nd lap and have T1 lap time. Then 40th lap on hards and have T2 lap time. T2-T1 say 2 seconds.
If then I run the same track and same fuel levels with softs. Will be difference same 2 seconds?

Are you talking a single stint?

If so, then the 2 sec difference will also be down to the significant fuel weight drop from lap 1 to lap 40.

If you are talking about just 40 laps of a race, then yes, it many cases the difference in lap time can be as much as 2s difference any any of the dry tyres due to rubbering, its one of the reasons you should try avoid burning a load of kers at the start of a race to open a gap, it can be pegged back too easily.

No. I am not talking about a single stint.

Imagine again the same situation.

60 laps race.
I have 4 stints with 15 laps each stint.
Same hard tyres and fuel levels every stint.
Temperature is the same through all the race.

2nd lap time is the 2nd lap of the 1st stint. Lap time is T1.
Then take 4th stint. Take the 2nd lap of 4th stint it is the 47th lap of the race. Lap time is T2. Let's assume T2 is 2 seconds less than T1 because of more rubber on the track and more grip.

Now take the same situation, only we have Softs.
Will be the difference between T2 and T1 also 2 seconds? Or the difference will be bigger or less than 2 seconds for softer tyres?

Did you test it (with numbers)? Or just suggesting?