Two Vehicle Model  

An example of a physics problem which requires the solution of simultaneous equations, this problem has one vehicle start from rest as a second vehicle passes it. The first vehicle is accelerating while the second is traveling at constant velocity. At what point (time and distance) will the two pass again?

After the velocity and acceleration models have been built, this is a natural extension, though students have to be led to the realization that there are now two objects and each requires its own set of stocks and flows. Once they picture that, they seem to be able to build the model.

Vensim PLE Software or STELLATM software is needed to create the model.

[Diagram Level | Equations Level | Graphs ]

Car_Distance(t) = Car_Distance(t - dt) + (Rate_of_change_of_Car_Distance)* dt
INIT Car_Distance = 0
Rate_of_change_of_Car_Distance = Car_Velocity

Car_Velocity(t) = Car_Velocity(t - dt) + (Rate_of_Change_of_Car_Velocity)* dt
INIT Car_Velocity = 0
Rate_of_Change_of_Car_Velocity = Car_Acceleration

Truck_Distance(t) = Truck_Distance(t - dt) + (Rate_of_change_of_Truck_Distance)
INIT Truck_Distance = 0
Rate_of_change_of_Truck_Distance = 21
Car_Acceleration = 6

Time Specs Settings
Standard: Range 0-12, dt = 0.25, Integration Method = Euler's

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