I have studied this one for several years now so allow me to offer my version.
The formulae I have seen are correct. I am going to stay as far away from them as possible for those less inclined.
Acceleration
Acceleration of a car depends on many factors, not just HP (power) or Tq (torque). Real life vehicle acceleration depends on:
1. Mass (how heavy the car is)
2. Torque (how much rotating force the ENGINE can deliver)
3. Gearing (how much rotating force the POWERTRAIN can actually deliver to axle)
4. Tire (how much of the final rotating force can rubber transfer to asphalt)
5. Surface (how much friction can the surface provide against the tire)
6. Driver (how fast can he/she efficiently manipulate 2 & 3 above?)
As you can see neither Tq nor HP determines how fast a car accelerates. Actually, do you see HP in the above list? Let me first elaborate on the above 1~5, 6 being pretty obvious.
1. Mass. This one is easy. Lighter the car, the faster it accelerates. That is, if 2 cars have Tq but one is 800 kg and the other is 1000 kg, then the 800 kg car will accelerate faster.
2. Torque. This one can be easy but not. Torque is a rotational force. When you screw in a bolt you are applying torque or rotation with force. Engine provides rotational force. Engine also has a torque band. Torque band is a range of RPM at which the engine provides most of its maximum torque. Therefore, 215 ft-lbs @3500 RPM does not paint the whole picture. Important thing is at what range does the engine provide 90% of 215 ft-lbs or torque? An engine with a broad torque band may produce this torque from 2000 ~ 6000 RPM. An engine with a narrow torque band may produce same torque from 2500 ~ 5000 RPM. This is called a 'peaky' engine. In general, an engine with a shorter stroke with bigger cylinder bores tend to be peaky with high RPM (JPN cars). In general, an engine with a longer stroke with smaller cylinder bores tend to be broad torqued (NA, European cars). Now, I say 'general' so don't quote me on it. Enough about torque so I'll get to shifting into 'powerband' as well as power later.
3. Gearing. This is also pretty easy but not easily understood. See, engine does not have enough torque to move engine when the car is stationary. That is why the engine stalls if you let out clutch suddenly. Let's take example of 700 Nm. If you think about it, that's not very much torque. 700 Nm is roughly 70 kg of mass hung on a stick 1 m long. Do you really think a man (weighing 70 kg) hanging at the end of 1 m long is sufficient to accelerate a 1500 kg car? Like a bicycle maybe! What you need is gearing. Gearing MULTIPLIES the engine torque. Now, there are 2 gear sets. The 'DRIVE' gear that the driver manipulates, and the 'FINAL' gear at the differential for RWD. When you hear 5 speed or 6 speed, it is referring to the number of 'DRIVE' gears. A 6 speed gear may have 4.35 (1st), 2.50 (2nd), 1.60 (3rd), 1.23 (4th), 1.00 (5th), and 0.85 (6th) with the 'FINAL' gear of 2.93. 6th gear has ration less than 1.0. This is called 'OVERDRIVE'. What this really means is that the transmission output shaft is rotating FASTER than the engine crankshaft. But what does all this mean when it comes to torque? It means that 700 Nm of ENGINE torque will become 700x4.35 Nm = 3045 Nm. Now we are talking! But that's not it. 3045 Nm of transmission output torque is further multiplied by the FINAL gear ratio of 2.93 which is 3045x2.93 Nm = 8922 Nm! This is of course divided between the 2 driving wheels so each driving axle delivers 8922/2 = 4461 Nm (or about 450 kg hanging off 1 meter long stick) or torque. A tire is about 0.6 m in diameter. So each driving tire will see about 4461 / 0.6 = 7435 N of force. Or the car is 'virtually' feeling 7435 x 2 = 14870 N of push or approximately 1500 kg of push. Say, wasn't that the mass of the car? That means Engine-Drivetrain combo is 'capable' of providing 1g of acceleration, fascinating! Going back to shifting using gear ratios above, if you are driving at 4350 RPM (4.35 1st gear ratio) and shift to 2nd gear, you would fall at about 2500 RPM (2.50 2nd gear ratio). If you are getting good torque at 2500 RPM, great. If not, you would need to drive at higher 1st gear RPM before shifting. For normal city driving, 3000 RPM is good. For competition in stock gear, the transmission is designed so that if you upshift near redline, the next gear would fall generally in 'good' torque band. For competition in racing gear, you would want to set it up so every upshift would land the gear within the torque band. This is why a broad torque band is good.
4. Before I get too excited and forget about what I am talking about, let's move onto Tires. 1g of acceleration typically this does not happen because the tire cannot deliver 7435 N because the tire physically cannot. I think a typical tire can provide about 1.2 times of force acting on it. So for a 1500 kg car, ideal front-rear 50%-50% distribution, each tire will be supporting 1500x0.5 / 2 = 375 kg or about 3750 N of weight. Therefore each tire can only generate 3750 x 1.2 = 4500 N of push. So we have approximately 3000 N of excess force, which goes to 'burning rubber'. In real life, a race tire will give you higher grip or say a factor of 1.5 (this is called friction coefficient). Also, aerodynamic downforce puts more 'weight' on each tire, therefore increasing grip. Therefore, spinning your tire does not give you better acceleration. However, it does heat up your tires which allows the tire to become more 'sticky' or provide higher friction coefficient.
5. Surface. A tire cannot have a coefficient of friction against air. CoF is always between 2 surfaces, never by itself. Afterall, you cannot clap with one hand no matter how many Zen monks tell you otherwise. A tire on ice will have different CoF than on asphalt. On watery ice, the CoF will be close to zero. Therefore you have to apply very gentle throttle and brake. So, why then does a wide summer tire not good for snowy winter roads? Isn't wider the better? Not really. In summer, you want the wide tires so the tire to road contact force is as low as possible. This allows better grip. On snow however, having a wide contact surface is not good because it will slip more easily. Therefore you need special grooves on the tires as well as narrower tires to provide 'mechanical' grip. (this is different mechanical grip that race drivers/engineers talk about). Therefore in summer, you have to rely more on rubber compound for grip, and rely on tire tread designs in winter as well as compound for grip.
I am tired. If you need more info, go do a research . . .
Before I finish, I have to complete the never ending argument between power and torque. Torque, is a physical thing that you can actually feel. Go twist your arm right now. That's torque. Power is not as intuitive. Power is actually torque multiplied by rotational speed (often expressed in RPM). Therefore 700 Nm of torque at 2000 RPM has twice the power than the same torque at 1000 RPM. Think of car as a 100m sprinter. Amount of 'push' that the sprinter can deliver is torque. How fast the sprinter can move his legs is power. A skinny legged runner that can move his legs very quickly can be fast. So can a muscular runner that can cover more distance with each stride. They both have same power. Which is better? There is always an ideal balance and each application requires different attributes, eg. marathon, 100m sprint, 1000m, cross country, etc.
Therefore, is it torque or is it power? Neither. It is a combination of above factors. A lighter, lower HP, better torque characteristics and gearing WITH a better shifting driver can always outdrive a lesser high HP car.
My verdict is, "It's not how fast the car is capable of, it's 'WHAT' the driver can get out of the car."
Meow! (='.'=)
