How Far Can a Car Travel When Accelerating from 0-81 mph?

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A car accelerating from 0 to 81 mph cannot be precisely calculated due to varying acceleration rates between different speed ranges. The acceleration from 0-60 mph differs from that of 0-100 mph, complicating the estimation. Using the provided data, an average acceleration suggests it would take approximately 271.37 meters, or 890.3 feet, to reach 81 mph. This estimate considers that the final speed impacts the acceleration rate, particularly due to factors like aerodynamic drag. Therefore, while an estimate can be made, the exact distance remains uncertain.
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A car can accelerate 0-60 mph in 8.6 seconds and 0-100 mph in 26.1 seconds. How far (in feet) would the car have to travel in order to accelerate from 0-81 mph?
 
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The acceleration rate from 0-60 mph is different than the acceleration rate from 0-100 mph. You could assume that the rate of acceleration is inversely proportional to the final speed (linear), but that really isn't the case with cars. So, with the given data, this problem is not solvable. The best you can do is find an estimate.
 
When I was first presented with the "Equations of Motion" I clearly hadn't been listening to 'Sir' well enough and I got very cross about just this point. I just thought ":How could you possibly tell?".
It took some time to take on board the qualification 'uniform acceleration'.
 
zgozvrm said:
The acceleration rate from 0-60 mph is different than the acceleration rate from 0-100 mph. You could assume that the rate of acceleration is inversely proportional to the final speed (linear), but that really isn't the case with cars. So, with the given data, this problem is not solvable. The best you can do is find an estimate.

What would the estimate be then?
 
Averaging the acceleration yields a result of 271.37m to reach the 81mph (36.21m/s).
It is a rough estimation, given that it should take more time to get that extra 19 mph from 81 to 100 mph than the 21 mph from 60 to 81 mph. Aerodynamic drag is proportional to the speed squared.
 
BTW:
271.37 m = 890.3 ft
 

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