import math

# Constants and parameters
P_max = 6500 # kW
eta = 0.9
rho = 1.2 # kg/m^3
A = 13 # m^2
Cd = 0.3
m_train = 860000 # kg
m_loc = 20.5 # tonnes
m_coach = 35 # tonnes
n_coaches = 24
m = m_train + m_loc + n_coaches * m_coach # Total mass of the train
g = 9.81 # m/s^2
Crr = 0.002
k = 0.01 # constant for curvature resistance
r = 1000 # radius of curvature for a typical railway curve

# Calculate maximum speed using the equation from before
v_max = math.sqrt((2 * P_max * eta / (rho * A * Cd)) - (2 * m * g * math.sin(0) / (rho * A * Cd)) - (Crr * g * math.cos(0)) - (m * v_max**2 * k) / (r * g))
v = 0
while v < v_max:
    F_res = (0.5 * rho * A * Cd * v**2) + (Crr * m * g * math.cos(0)) + (m * v**2 * k) / r
    F_grade = m * g * math.sin(0)
    a = (P_max * eta - F_res - F_grade) / m
    v += a * 0.01 # Use a small time step of 0.01 seconds for numerical integration
    print(f"Velocity: {v:.2f} m/s, Acceleration: {a:.2f} m/s^2")