The friction coefficient of Formula 1 car tyres are around 1.7 in dry weather. Assuming sufficient power from the engine, calculate the theoretical best 0-100 km/h acceleration time in seconds. (neglect downforce, g=9.81m/s^2)

We have to appreciate the assumptions we are working with. The problem states that power is available infinitely, therefore the maximum acceleration influencing factor is the tire grip. It is reached when the tire doesn't yet slip on the asphalt, but operates at its maximum friction coefficient, to achieve max force. An other assumption is that as the car accelerates no downforce is created by the fins, so the weight of the car on the asphalt is constant.

We start with a sketch to visualize the problem, identifying the body that is accelerated. We create an FBD, a free body diagram.

We are not given too much information about the car itself, but that shouldn't hold us back. Let the car's mass be little m (unknown).

At this point we can identify the forces acting on this mass. Gravity W=mg, and F(friction)=F(normal to ground)mu(friction) The normal force in this case will be the weight of the car, mg. Hence the accelerating force F(friction)=mg*mu(friction)

As an accelerated mass, we can apply Newton's law of motion, F=ma. As the accelerating force is F(friction), plugging F(friction)=F we have mgmu(friction)=ma We can simplify by dividing down by the unknown mass "m", and rearrange to get acceleration as a=g*mu(friction)

Converting 100km/h to m/s is dividing by 3.6, therefore v=100/3.6. This speed is reached in time t=v/a

Plug the above equation into our acceleration equation to get t=v/(g*mu(friction))=1.67 seconds.

So the answer to this question is the following. With the tires provided the theoretical best acceleration time from 0-100 km/h is 1.67 seconds, assuming power is available and no downforce is generated.

(Additional note: Actual Formula 1 cars trimmed for race conditions don't achieve this number, they accelerate in around 2.1-2.7 seconds. However the quickest recorded time on conventional tires is 1.60 seconds, reaching theoretical ultimate. As a bonus question, think about what could be done to further improve on this result!)