How fast do F1 cars accelerate?

Well if you generaly refer to any F1 car, first thing you must take into consediration is POWER/WEIGHT ratio

Since F1 car weighs 702 kg and has 950+ HP engine, it has power to weight ratio around 1,400 hp/ton

Let’s see how power to weight ratio compares to other supercars :

Bugatti Veyron : 523 hp/ton

Nissan GT-R : 293 hp/ton

Ferrari Enzo – 418 hp/ton

McLaren F1 – 489 hp/ton

Compared to an F1 car, this numbers seem tiny in comparison.

Since Bugatti Veyron can reach speeds over 400 km/h with only 523 hp/ton, F1 cars can theoretically reach speeds of 500(310 mph) and even 600 km/h(372 mph) if driven with zero downforce. 

However, they can only reach about 370–80 kph (260 mph) because they are setup with EXTREMLY high downforce, wich reduces top speed dramatically, but in turn allow extreme cornering speeds. 

F1 car can turn at around 5–6 G. Buggati Veyron can’t even corner at 1.5 G. For example Blanchimont corner at Circuit de Spa Franchonchamps. F1 cars negotiate that corner flat out well above 300 km/h. Bugatti veyron must slow down to 130 km/h otherewise it will crash.

If you drive a F1 car with zero downforce, it would be theoretically possible to reach 500, even 600 km/h but without downforce the car is very unstsble at that speeds and you will most likely crash. 

Since they have extreme power to weight ratio they are intentionaly setup with EXTREME downforce which reduces top speed EXTREMELY to allow EXTREME cornering speeds, since no track in world has long enough straight to reach that speeds and sustain that speeds. Hope this was helpful