how does the air intake work exactly and how does it affect the acceleration for the car..
the air intake supplies the engine with the air necessary for gas combustion (read explosion). the more oxygen your car gets, the better the explosion, which creates more power. that equals better acceleration.
Most importantly though the air fuel ratio must be understood when dealing with an intake. See air/fuel is all about air density not volume. There is a certain point that the air volume can be increased to a level that makes the car operate poorly. 2 ways to improve air density: Make it Cold eg: intercooler, cold air intake Force it eg: turbocharger, supercharger, Ram air intake. This is all an issue of physics when air molecules are cooled they are less active take up less space and pack together better. the same thing generally happens to air molecules when they are pressurized but the rate at which heat is lost when air is pressurized to say 15psi is marginal so a combination of the two is usually used when trying to increase a cars performance. To the acceleration issue. Oxygen is an oxidizer works in the same way as say nitrous oxide. Except it is abundant and we don't have to keep it in a canister. Components of fire are something to burn and an oxidizer 90% of the time that oxidizer is air. Those rare alternatives are like thermite or sulfer flares usually sulfer iron oxide or potassium and aluminum filings. Iron or potassium act as your oxidizers in these cases. So the more oxidizer we add the better the fuel is consumed. like blowing into a fire or across hot coals. Of course the octane rating of your fuel source has something to do with this as will as it is an indicator of how fast or clean of a burn you will get in these circumstances. Octane is the resistance of a fuel to detonate. Why do you want that well your engine is very hot and you want the fuel to burn when you say not when it feel hot enough to do it. A high octane fuel and denser air will combust faster and more completely thus creating more rapid expansion on the piston. So throttle response generally improves because the detonation is more stable and acceleration is increased to the more rapid combustion of the same amount of fuel. Warning too much air can cause your car to compensate with more fuel and sometimes your car will put out too much fuel and you can actually lose power instead of gain it. If installing an intake modification follow the manufactures method for reseting the default fuel map unless using a standalone or piggyback engine management system. This will force the car to take the readings of the new denser air as the standard and not some sudden change in air temperature since air density is usually calculated by temperature extra cold air can have short term undesirable effects on fuel economy.