Can the same car with 100HP and 500HP produce the same acceleration on first gear? My friend and I are debating about the acceleration of cars in first gear. He said that the same car (weight, tires, etc) produces the same acceleration with both 100HP and 500HP. I imagine that the moment when the tires catch the surface of the road both start with the same speed at moment 0, but the one with 500HP will have a higher acceleration in the next moment because it manages to spin the tires faster than the other one.
If someone can explain me a little about this can be great.
 A: I suspect that your friend's argument is based on the limits of traction. 
There is a maximum force a tire can transfer to the car before it starts skidding. Skidding reduces the amount of force delivered so drastically that it basically doesn't matter how fast you spin the wheel, it will always loose against a wheel at threshold grip. 
The amount of traction depends on 


*

*tire dimensions

*tire pressure

*tire profile

*amount of tires that touch the ground (relevant for strong turns) 

*road type (tarmac, asphalt concrete, dirtroad, etc.)

*road conditions (wet/dry, sandiness, etc.)

*weight on the wheel (rear wheel drive is better than front wheel drive for this sort of thing )

*...and a bunch of other factors


A reasonable explanation is given here, here and here (all on the same site).
So, when given 2 otherwise identical cars, under the exact same conditions, with the exact same (and experienced) driver:


*

*If the 100 HP car can already cause wheel spin when flooring it, the extra 400 HP will not contribute much to the initial acceleration

*If the 100 HP car can not cause wheel spin, the extra 400 HP will be beneficial. 


More powerful cars (greater HP-to-weight ratio) usually also have different gear boxes to make more effective use of all this power. Usually, the 500 HP car is able to accelerate for much longer before you need to change gear. 
Related: the engine/gearbox combination has a specific curve for the amount of torque on the wheels vs. engine RPM. Normally, the higher the RPM, the more power you waste (mostly due to internal friction). The 500 HP car will be much more likely to be able to sustain threshold acceleration for much longer than the 100 HP will. 
So, when constantly applying threshold acceleration to your two cars, the 500 HP car will reach 100 km/h far quicker, due to these differences. Power does matter, but during those first few seconds, it's really the driver's experience that matters :) 
A: I am his friend :). This argument came up when we were discussing the G forces felt by our bodies in a smaller powered car (let's 90 hp) and a larger power one (400 hp). I said that the G forces are dependent on the amount of grip you can catch with your tires and assuming both cars are exactly the same in (body mass, tires, aerodynamics, front/rear wheel drive train) then you can achieve a fixed maximum G force for both cars (if the lower powered car can achieve skidding in first gear). The maximum G force is felt at the peak of the friction function graph (right before the skidding occurs - when there is a slight drop in the gripping power of the tires). This is the same principle followed in ABS  breaks design sistem. 
Therefore is my opinion that you will not feel large (peak) G force in the larger power car then in the smaller one because the smaller one can achieve that peak (for a shorter period of time thou) in first gear right before the wheels start skidding. The difference between the two cars will be noticed more on higher gear ratio acceleration. So let's say the "medium" of the G forces will be higher for the larger power car because it can sustain larger G forces for a longer period of time. But a "peak" G force can be felt by both cars.
A: Physicists tend to have a different way of looking at these things than mechanics, car buffs, and engineers. We look for simple models that abstract out as many nasty details as possible. Since this is a physics site, I'm going to give you one possible physicist-style model. I want to provide some insight into the problem by considering the simpler case where the transmission is continuous rather than having discrete gears. This means that the engine's power is a limiting factor, but not its torque. Of course the question refers to being in first gear, but I'm just going to translate that into a statement about speed -- we're interested in low speeds.
The road exerts a forward frictional force $F$ on the tires, and at speed $v$, this requires the engine to dissipate power $P=vF$. In the limit of low speed (like when you start from a stop sign or burn rubber), this power goes to zero. Therefore at low speeds, a car's acceleration is limited simply by the amount of friction. In the standard Amontons model of friction (which is not all that accurate for rubber tires, but again, the idea is to make simple models), the maximum acceleration is $\mu_s g$, which is independent of the engine's power.
So in this simplified model, the answer is that power doesn't matter, which is in agreement with Alex's answer. However, the simplified model may be an oversimplification. Cars do have discrete gears, and there is no guarantee that a given car's engine, in first gear, can provide enough torque to give the maximum acceleration $\mu_s g$. For instance, when I drove a pickup truck for the first time and wasn't used to its stump-puller gear ratio in first gear, I inadvertently burned rubber.
A: You are all complicating the issue - it's basically a matter of gearing & weight - what is the final drive ratio of the transmission? What is the gearing of first gear in each car? A car with incredibly high final axle gearing (like say 6:1 - most cars are around 2.73 to 4.19:1) and low horsepower could feasibly compete with a 500hp vehicle with an incredibly low gearing / axle ratio of say, lower than 1:1 - it's mostly about torque multiplication.
That being said, the 500hp engine is able to do more work - in physics terms - than the 100hp engine, and that is a factor in later acceleration and higher final speeds; engine design, flywheel weight, redline, torque and HP curves, piston size/design/weight, all of these are huge factors as well as the weight of the car and FWD vs AWD vs RWD.
Biggest physics factors are really weight and gearing (torque multiplication). A 1200 lb Atom Ariel with 250 hp is much faster to 60 and 1/4 mile than a 550 hp Mercedes CLS AMG for instance, or 650 hp Dodge viper. So are a number of 70-100 hp motorcycles. So it's not theoretical at all and completely feasible.
A: There are kind of two different physical cases we could talk about:


*

*Internal combustion engine cars

*Electric cars


The way that I understand the function of modern EVs, there are mostly no moving parts when the car is stopped and idled (except for possibly the AC).  This gets us much closer to the fundamental physical model.  For detail of this model, I would suggest Ben Crowell's answer.
However, this is a poor descriptor of gas-powered vehicles.  Those are required to have the engine constantly spinning as a matter of their design and thermal cycle.  That means that some amount of rotational momentum is always stored in the engine.
Again, we have to artificially limit the discussion, because not all cars have the same type of clutch.  However, manual transmission cars still exist, and the question is totally answerable for those.  If the clutch is engaged very quickly, then it's extremely easy to hit the wheel-ground traction limit.  In this case, it's not the power that is the limiting factor, but the stored rotational energy within the engine shaft.  Depending on the vehicle, it might not even be able to keep moving because the rpms will be too low once that shaft has combined with the wheels and forward momentum of the car.  However, it paints a picture of an infinitesimal moment where a car of any horsepower would be peeling out.
So my answer is to side with your friend, with the qualifier that it is a manual transmission, and that it's a meaningless accomplishment.  If its an automatic, the details will depend entirely on the mechanics of the transmission.  Anecdotally, I find it much harder to get the low-speed rubber burning with them.
A: Yes. 1st gear acceleration is usually limited by traction. So weight balance, cg height and tires drive 1st gear acceleration.
More power will just allow you to carry this acceleration to a higher speed. Meaning the shift to 2nd gear can be done at a higher speed. Like a Z06 corvette that does the 0-60 in one gear.
A: Power equals force times velocity; that means that the amount of force that can be achieved with a given level of power will be power divided by speed, and acceleration will thus be power divided by speed, divided by mass.  Note that in practice this equation doesn't mean that one can achieve nearly infinite acceleration with even a tiny amount of power, but rather that it's impossible to usefully direct significant power toward producing acceleration until the object has started moving.
If a vehicle with given tires and weight distribution is riding on a particular road surface, those factors will limit the amount of power that can be employed to accelerate the vehicle at any given speed.  Until the vehicle reaches a speed where the acceleration the tires can achieve exceeds the power the engine can produce, the engine's ability to produce power will be irrelevant.  Note that a "500hp" engine isn't capable of producing 500hp under all possible conditions; depending upon the designs of the engines and transmissions, it may be that the 100hp vehicle is able to put nearly 100hp of useful power to the wheels at a speed where the 500hp engine and transmission wouldn't be capable of producing that much (I would expect a typical 500hp vehicle would probably be able to produce at least 1/5 of its peak power in any case where the tires could convey that much, but some turbocharged vehicles might not).
While vehicles with larger engines are often capable of producing better acceleration even at lower speeds than those with smaller engines (in part because drivers who are willing to pay for larger engines often want good starting-line performance), acceleration at lower speeds is limited by factors other than engine power.  If the maximum acceleration the tires can produce at a given speed can be achieved with only 20hp, a 100hp and 500hp engine will likely perform essentially identically.
