import numpy as np

# 给定数据
t_values = np.array([0, 10, 15, 20, 22.5, 30])
v_values = np.array([0, 227.04, 362.78, 517.35, 602.97, 901.67])

# 确定插值区间，选择包含 t=16 的四个数据点
t0 = t_values[1]  # 10
t1 = t_values[2]  # 15
t2 = t_values[3]  # 20
t3 = t_values[4]  # 22.5

v0 = v_values[1]  # 227.04
v1 = v_values[2]  # 362.78
v2 = v_values[3]  # 517.35
v3 = v_values[4]  # 602.97

# 构造Lagrange插值多项式
p = v0 * ((16 - t1) * (16 - t2) * (16 - t3)) / ((t0 - t1) * (t0 - t2) * (t0 - t3)) + \
    v1 * ((16 - t0) * (16 - t2) * (16 - t3)) / ((t1 - t0) * (t1 - t2) * (t1 - t3)) + \
    v2 * ((16 - t0) * (16 - t1) * (16 - t3)) / ((t2 - t0) * (t2 - t1) * (t2 - t3)) + \
    v3 * ((16 - t0) * (16 - t1) * (16 - t2)) / ((t3 - t0) * (t3 - t1) * (t3 - t2))

# 计算 t=16 时的速度
velocity_at_16 = p

print(f"使用Lagrange插值法，t=16 秒时的速度为: {velocity_at_16:.2f} m/s")