Is speed better, or is acceleration better? [closed]

The answer to this is: it depends, specifically, on the layout of the track. I'm providing a universal answer here, not specifically tailored to the quirks of Forza-5 (this applies to most racing games save some very old 8-bit ones that use bit-hacks instead of properly doing accelleration).

A thought experiment:

You can simplify how to think about the problem by a simple scenario: a drag race. Suppose two cars, car F and car X hold a drag race.

Car F is the fastest, but car X has better accelleration. To simplify complex physics1, we assume the accelleration is constant until top speed is hit. Plugging in some (fake) numbers:

Car      Topspeed                Accel        
Car F    100 m/s (360 km/h)      5 m/s^2
Car X    80 m/s  (288 km/h)      8 m/s^2

You can solve to get two distance functions:

df(t) = 2.5t^2       t <= 20
        100t - 1000  t >= 20
dx(t) = 4t^2         t <= 8
        80t - 400    t >= 8 

Some basic logic suggests that car X will be passed by car F after both hit top speed (80 * 20 - 400 = 1200 > 1000). Solving for:

80t - 400 = 100t - 1000 => t = 30

In other words, in 30 seconds, after travelling 30 * 80 = 2400m car X is overtaken. This means the faster car wins a longer drag race than this, e.g. a 3km race, but would lose a shorter race such as a 2km race.

How does this translate to a track?

You might ask, what does a drag race have to do with how such a car performs on a complex twisty track? You can see such a track as a series of straights and turns. You accellerate on the straights, then break just enough to make each turn. This makes each straight section into its own mini-drag race (although with a head start on speed). This then leads to the following rule of thumb:

  • On a track with shorter straights accelleration is more valuable.
  • On a track with longer straights top speed is more important.
  • Grip can substitute for accelleration in particular with sharp corners and short straights (you get more value out of being able to turn at a faster speed the more turns there are).

Notes

1 How complex the physics are will vary from game to game, you'd have to look into its code to figure out how it's handling air resistance and tyre friction for a true comparison. For this higher-order ODE there's no exact solutions, only simulations and approximations.

In a highly realistic racing game air drag will be simulated, and cars have a complex accelleration curve. However, this curve will have a similar shape, so the above points still hold. It's just much harder to calculate when which car comes out ahead.