Relationship between acceleration and distance

[karabiner98k]

I have a magazine test of Audi RS4 and Mitsubishi Lancer EVO IX.
There is something interesting in this test.
RS4 does 0-100km/h in 4.7 (s) in a distance of 78.3 (m)
EVO does 0-100km/h in 4.7 (s) in a distance of 74.7 (m)

Does it mean that EVO is faster despite having similar acceleration time?

What is the relationship between acceleration and distance??

 

[rcgldr]

Assuming the times and speeds are identical, what it means that at 4.7 seconds, the RS4 is 3.6 meters ahead of the EVO, and that both are going 100 kmh. The RS4's average speed during that 4.7 seconds would be slightly higher, since it covered 3.6 more meters. It implies that the RS4 accelerated better early on, and the EVO accelerated better later on in order to achieve the same speed at the same time. If you plotted speed versus time for both cars, the area under the curve for RS4 is 3.6 meters greater than the area under the curve for the EVO. This could be related to gear shifts. You'd need more sample points to know what the actual trend was.

 

[karabiner98k]

Assuming the times and speeds are identical, what it means that at 4.7 seconds, the RS4 is 3.6 meters ahead of the EVO, and that both are going 100 kmh. The RS4's average speed during that 4.7 seconds would be slightly higher, since it covered 3.6 more meters. It implies that the RS4 accelerated better early on, and the EVO accelerated better later on in order to achieve the same speed at the same time. If you plotted speed versus time for both cars, the area under the curve for RS4 is 3.6 meters greater than the area under the curve for the EVO. This could be related to gear shifts. You'd need more sample points to know what the actual trend was.

Thanks for your answer.
Does it mean that in a drag race EVO is ahead of RS4 up to 100km/h because it needs less distance?

Here are more sample points:
RS4 0-60km/h 2.26 (s) in 22.1 (m)
EVO 0-60km/h 2.41 (s) in 22.5 (m)

RS4 0-80km/h 3.43 (s) in 44.7 (m)
EVO 0-80km/h 3.53 (s) in 43.9 (m)

 

[rcgldr]

Does it mean that in a drag race EVO is ahead of RS4 up to 100km/h because it needs less distance?

It means that the RS4 is ahead because it initially accelerates faster than the EVO, and that later the EVO accelerates faster than the RS4. Your additional sample points show this is what happens. The RS4 acclerates 0 to 60 kmh .15 seconds quicker than the EVO (2.26 seconds versus 2.41 seconds). The EVO accelerates from 60 kmh to 80 kmh .05 seconds quicker than the RS4 (1.12 seconds versus 1.17 seconds). The EVO accelerates from 80 kmh to 100 kmh .10 seconds quicker than the RS4 (1.17 seconds versus 1.27 seconds), and now has the same speed, but is still 3.6 meters behind the RS4.

 

[karabiner98k]

It means that the RS4 is ahead because it initially accelerates faster than the EVO, and that later the EVO accelerates faster than the RS4. Your additional sample points show this is what happens. The RS4 acclerates 0 to 60 kmh .15 seconds quicker than the EVO (2.26 seconds versus 2.41 seconds). The EVO accelerates from 60 kmh to 80 kmh .05 seconds quicker than the RS4 (1.12 seconds versus 1.17 seconds). The EVO accelerates from 80 kmh to 100 kmh .10 seconds quicker than the RS4 (1.17 seconds versus 1.27 seconds), and now has the same speed, but is still 3.6 meters behind the RS4.

Thanks but there is still something i don't understand
Suppose that 0-60km/h and 0-80km/h and 0-100km/h times are the same for both cars.
But 0-100 km/h distances are different RS4 78 (m) vs EVO 74 (m).
Does it mean that for example in a distance of 74 (m) RS4 reaches about 97 or 98km/h?

 

[rcgldr]

Suppose that 0-60km/h and 0-80km/h and 0-100km/h times are the same for both cars. But 0-100 km/h distances are different.

If the times are the same, then the distances will be the same.

Does it mean that for example in a distance of 74 (m) RS4 reaches about 97 or 98km/h?

More like 99.4 km/h, since it reaches 100 km/h 3.6 meters later, which is only about .036 seconds later.

 

[karabiner98k]

So, if only 74 (m) available, EVO could be faster with more speed in the end?

 

[rcgldr]

So, if only 74 (m) available, EVO could be faster with more speed in the end?

The RS4 reaches 74.7 m before the EVO does. When the RS4 reaches 74.7 m, at about 4.664 seconds, the EVO has reached about 71.7 m, the RS4 is going about 99.43 km/h, the EVO about 99.38 km/h. About .036 seconds later, at 4.700 seconds. the RS4 reaches 78.3 m, the EVO 74.7 m, and both cars are going 100 km/h. Until 4.700 seconds, the RS4 is gaining distance on the EVO, ended up 3.6 meters ahead at 4.700 seconds. If the EVO continues to out accelerate the RS4 after 4.7 seconds, then it will start gaining on the RS4 and eventually pass it.

It's a case like this that shows that distance to speed is not a good indicator of overall performance without knowing time to speed as well. If you had a graph showing speed versus time during acceleration, you could calculate distance versus time by integrating (the area under the speed versus time curve is distance), and you could take the derivative to determine acceleration versus time (acceleration is the slope of the curve at any point in time).

Distance to speed is mostly a useful bit of information for an aircraft that needs to reach takeoff speed within a certain distance.

 

[karabiner98k]

The RS4 reaches 74.7 m before the EVO does. When the RS4 reaches 74.7 m, at about 4.664 seconds, the EVO has reached about 71.7 m, the RS4 is going about 99.43 km/h, the EVO about 99.38 km/h. About .036 seconds later, at 4.700 seconds. the RS4 reaches 78.3 m, the EVO 74.7 m, and both cars are going 100 km/h. Until 4.700 seconds, the RS4 is gaining distance on the EVO, ended up 3.6 meters ahead at 4.700 seconds. If the EVO continues to out accelerate the RS4 after 4.7 seconds, then it will start gaining on the RS4 and eventually pass it.

Here is the end of the test:
RS4 0-140km/h 8.52 (s) in 204 (m)
EVO 0-140km/h 9.31 (s) in 225 (m)

RS4 0-160km/h 10.98 (s) in 307 (m)
EVO 0-160km/h 11.62 (s) in 322 (m)

What does it mean?

 

[rcgldr]

What does it mean?

The RS4 out accelerates the EVO from 0 to 60 km / h. The EVO out accelerates the RS4 from 60 km / h to 100 km / h. The RS4 out accelerates the EVO at some speed a bit above 100 km / h. Probably related to the gearing in the cars, and perhaps aerodynamic drag differences.

 

[karabiner98k]

The RS4 out accelerates the EVO from 0 to 60 km / h. The EVO out accelerates the RS4 from 60 km / h to 100 km / h. The RS4 out accelerates the EVO at some speed a bit above 100 km / h. Probably related to the gearing in the cars, and perhaps aerodynamic drag differences.

RS4 travels 307m in 10.98s
EVO travels 322m in 11.62s

So, in 10.98s EVO travels about 310m or so.

How can RS4 out accelerate EVO by traveling less distance in 10.98s??
This is the part i don't understand.

 

[dgOnPhys]

I have a magazine test of Audi RS4 and Mitsubishi Lancer EVO IX.
There is something interesting in this test.
RS4 does 0-100km/h in 4.7 (s) in a distance of 78.3 (m)
EVO does 0-100km/h in 4.7 (s) in a distance of 74.7 (m)

Does it mean that EVO is faster despite having similar acceleration time?

What is the relationship between acceleration and distance??

Trying to make a comparison using data taken at the same velocity is somewhat involved. It is a lot easier to plot distance versus time and compare the graphs (see attachment). As you can see the RS4 is consistently ahead of the EVO even if their accelerations compare differently along the track.

The velocity is the first derivative of the curve (slope), acceleration its second derivative.

 

[karabiner98k]

Trying to make a comparison using data taken at the same velocity is somewhat involved. It is a lot easier to plot distance versus time and compare the graphs (see attachment). As you can see the RS4 is consistently ahead of the EVO even if their accelerations compare differently along the track.

The velocity is the first derivative of the curve (slope), acceleration its second derivative.

Thank you so much for the PDF.
So, in 10.98s AUDI travels more distance than the EVO.