Equations

The Formula 550 is a race. You play Acceleration cards in order to change your velocity and then use the average velocity for your turn in order to determine the distance that you travel.  In order to simplify the Physics of the game, we assume that the direction that you are traveling is not relevant and so the equations for straight-line motion apply.  

Throughout the discussion we use the terms "velocity" and "speed" interchangeably.  By strict definition these two terms are not identical.  "Speed" is a measure of how fast something is moving while "velocity" is a measure of how fast something is moving AND in what direction.  However since we have assumed straight-line motion for analysis purposes, the direction is not relevant and these terms are essentially the same.

Acceleration is defined as the change in velocity divided by the change in time:

a = (V_f - V_o)/(t_f – t_o) = (V_f – V_o)/t if t_o = 0 where:

V_f is the final velocity (at the end of your turn)

V_o is the initial velocity (at the start of your turn)

a is the acceleration (during your turn)

t is the time, either 1, 2, or 4.

This equation can be rewritten to determine your final velocity due to your acceleration:

(1) V_f = V_o + at

The average velocity for your turn is given by:

(2) V_ave = ½(V_o + V_f)

The distance that you travel during your turn is given by:

(3) d_turn = V_ave t

The distance that you travel during your turn can also be determined using equation (4) without calculating your average velocity. Equation (4) can be derived from equations (1) to (3).

(4) d_turn = V_ot + ½ at²

Your total distance traveled, or your position x equals the position at the start of your turn plus the distance traveled during your turn.

x = x _{previous turn} + d_turn

Example

We will illustrate how the equations are applied by discussing an example. Assume that you start the game by playing an Acceleration = 40 card. Since you have just started, your initial velocity is zero. The time for your turn equals one.  Your new velocity is found using the following equation:

V_f = V_o + at = 0 + 40(1) = 40

This final velocity is your velocity at the end of your turn. Your average velocity for the turn is found using:

V_ave = (V_o + V_f)/2 = (0 + 40)/2 = 20

The distance that you travel during this turn is found using:

d = V_avet = 20(1) = 20

Your new position is found using:

x = x _{previous turn} + d = 0 + 20 = 20

Discussion of Units

Throughout the discussion we have referred to distance, velocity, and acceleration. We have also mentioned a distance of 550.  However we have never mentioned the units for these variables.  Whenever you hear a number or variable you should generally ask about its units. For a number without units is just about meaningless.  So if units are so important, why did we leave them out? We decided that you or your teacher should choose the units that you prefer. Some schools emphasize metric units and others emphasize English units.

In the Formula 550 you can use any units that you want.  For distance, the units of miles or kilometers probably makes the most sense since automobile races are generally measured in terms of miles or kilometers.  The other unit we need is for time.  During the game you will accelerate and travel a certain distance during your turn.  Therefore, you can make the unit of time be your "turn".  Alternately you could decide that each turn takes a certain amount of time such as an hour.  Then the unit for time would be "hour".