Clarifications And Hints On LAAS Math Contest Questions


Los Alamos Academy of Scientists

On January 29, an article was published: ( ) about US education, and a contest was proposed for students and professors to solve it: );  

The answers to problems have to be sent by e-mail with the subject “Insane Acceleration Cars” to

Deadline for the contest is now March 18 and prizes  are:

$200 – 1st place – 5 questions solved and pertinent explanations
$100 –2nd place or 4 question solved and valuable comments;
$50 – 3rd place
$10 gift cards for Smith’s will be presented to 5 honorable mentions.

The problem was inspired from real life applications, as driving a car on asphalt or ice; adhesion forces are combined with aerodynamics; cars are able to fly on the ground.

I was sorry to learn that this problem about driving and friction forces is not taught in our schools although it affects 90% of our daily life’s events, and even more. The problem is not putting too much importance on arithmetic and algebra in spite it is preferred to be done right without errors, but on phenomenological understanding, and that is why numbers are simplified as much as possible, like:

mass=1ton=1000 kg; wheel perimeter = 1m; Power=10 MW; g=10; µ=1; Aerodynamic drag = 0.2 along longitudinal direction and 0.5 transversal direction, test in Los Alamos where air density is about 1 kg/cubic meter, etc. see that problem at link:

  ( )

The problem is as follows:

1a – find the acceleration, speed and space variation with time for the vehicle as seen on vehicle’s regular speedometer, and as seen from outside the vehicle, (or, say, indications of a smart GPS onboard), without considering any aerodynamic drag force.

1b – the same problem with drag force

  1. Was ill posed, because it will create a disadvantage for girls, who had a different education and are not so interested in high performance vehicles’ science beyond, and to make the student waste his time to identify vehicle was not intended but to find its performances – power, speed, acceleration, mass and put that in equation too.

The vehicle is Lamborgini Evo and can be easy found by a goggle search:

but here it is:  

“The Evo features a 5.2-liter 10-cylinder engine that outputs a massive 640 horsepower (470 kW) and 443 pound-feet (600 Nm) of torque. These come at 8,000 and 6,500 rpm respectively and push a vehicle whose dry weight is a mere 3,135 lb (1,422 kg) – that’s about 4.9 pounds per horsepower. The boosting and lightweight components of the engine come thanks in part to a titanium intake and lightweight exhaust.

Power still comes from a 5.0-liter V10 in the Performance, but Lamborghini has managed to free up another 38 hp (28 kW) over the standard car for peak power of 640 hp (477 kW) and peak torque of 600 Nm. The 100 km/h (62 mph) sprint takes just 2.9 seconds, and the car doesn’t stop pulling until the needle is north of 325 km/h (202 mph).”

The intended question may be reformulated like that:

  1. Use the data from Evo and calculate acceleration, speed, space variation and explain the differences obtained with and without aerodynamic drag force.
  1. Same as 2 but for another car: Aston Martin’s Valkyrie :

“The car contains a 6.5-litre naturally-aspirated V12 engine tailored by Cosworth, which was initially planned to produce around 1,000 hp (746 kW; 1,014 PS), but it was later announced in June 2017 that the engine would produce 1,130 hp (843 kW; 1,146 PS) @ 10,500 rpm with a redline of 11,000 rpm. At the same time the power output was released, the weight was also mentioned, at 1,030 kg (2,271 lb), which surpasses the intended 1:1 power-to-weight ratio, with 1,097 hp (818 kW; 1,112 PS) per ton, achieving a zero to 60 mph (97 km/h) time of 2.5

seconds; speed 250 mph = 402 km/h = 112 m/s” The emphasis was on aerodynamics as presented in the video:  

But updated and customized to our problem  

Question 4: “If the Cy=0.5, the lateral surface is 5 m2 and cross wind is 20 m/s, in Los Alamos, what will be the movement of the vehicle accelerating forward after x direction? Cx, Cy are the aerodynamic coefficients for movement of air, x is forward, y is lateral and z is upwards, g=10 m/s2.”

Apply this to point 1a and 1b; one needs to analyze the lateral stability and behavior.

Because as I have recently learned from a reader that “this sort of physics is no longer taught in high-schools. One reason is that fast cars are thought to be more of interest to boys than to girls. 30 – 50 years ago physics problems about fast cars were common, but now they are much less common”, I give a hint towards ellipse/circle of adhesion/friction and I recommend the following links as hints:  

This I hope may help students get the right solution to lateral movement.

Question 5 : “What power is reasonable for the vehicle and how it have to be applied in order to minimize the acceleration time?”

This question was intended to show that the power in Question 1 was uselessly high, and to reduce it at maximum needed to obtain maximum possible performance, and then to determine acceleration, speed space and power variation with time for the case with aerodynamic drag force and with and without lateral 20 m/s wind.

I think now one should have all the clues and that the lack of specific education in schools has been thus compensated.

Please speed-send solutions to, with title “insane acceleration vehicle”.

Deadline: March 18, 2019