#Ana Loureiro 104063

import sympy as sy
import numpy as np
import matplotlib.pyplot as plt

m = 0.05
x0 = 0.03
g = 9.8


#lei do movimento x(t) = x0 + v0*t + 1/2*ax*t^2
# v(x) = v0 + ax*t


P = m * g

#(a)
t = sy.symbols('t')
a = P # m/s²

v = sy.integrate(a, t) 
x = sy.integrate(v, t)

print("v(t) =", v)  
print("x(t) =", x)  


t_vals = np.linspace(0, 5, 100)
v_lam = sy.lambdify(t, v, "numpy")
v_vals = v_lam(t_vals)

plt.plot(t_vals, v_vals)
plt.xlabel('tempo (s)')
plt.ylabel('velocidade (m/s)')
plt.title('Velocidade da bola')
plt.grid()
plt.show()



x_lam = sy.lambdify(t, x, "numpy")
x_vals = x_lam(t_vals)

plt.plot(t_vals, x_vals)
plt.xlabel('tempo (s)')
plt.ylabel('posicao (m)')
plt.title('posicao da bola')
plt.grid()
plt.show()