im doing a physics lab and I’m trying to solve this system of equations:

(0.11551-0.002744*C*v^2)/0.2025 = dv/dt

v=ds/dt

C=322/3300v when 3300v<10

C=10^(3.02-1.89*log(3300v)+0.411(log(3300v))^2-0.033(log(3300v))^3 when 10<3300v<20000

C=0.74 when 3300v>20000

v is velocity, C is drag coefficient, s is distance traveled, t is time

I’m trying to write a python code to find t at s=0.75. t is about 1.6, but i just want to get a more accurate answer. inital v=0, t=0, s=0. s is distance, v=velo, t=time. s, v, t, and C can’t be negative

## here are some attempts (i’ve never coded in python before, i should probably learn some)

## I’m having trouble incorporating C into the equation for dv/dt. I can calculate C in the 1st one, but I can’t implement it into the main equation, and in the 2nd one, I can’t implement a piece-wise C into dv/dt.

from Solving Second Order Differential Equations in Python - ePythonGuru

```
from matplotlib import pyplot as plt
from scipy.integrate import odeint
import numpy as np
def f(u, x):
return [u[1], (0.11551 - 0.002744 * 0.74 * (u[1])**2) / 0.2025]
y0 = [0, 0]
xs = np.linspace(0, 10, 100)
us = odeint(f, y0, xs)
ys = us[:, 0]
plt.plot(xs, ys, '-') # Plot the line
plt.plot(xs, ys, 'r*') # Plot the points
plt.xlabel('x values')
plt.ylabel('y values')
plt.title('Updated Plot Title')
plt.show()
```

from chatgpt lol

```
from scipy.integrate import odeint
import numpy as np
import matplotlib.pyplot as plt
# Function representing the modified differential equation
def model(v, t):
# Calculate C based on the value of 3300v
if 3300 * v < 10:
C = 322 / (3300 * v)
elif 10 < 3300 * v < 20000:
C = 10**(3.02 - 1.89 * np.log(3300 * v) + 0.411 * (np.log(3300 * v))**2 - 0.033 * (np.log(3300 * v))**3)
else:
C = 0.74
# Your differential equation logic using v
# For now, returning v itself without using C in the equation
return 0.11551 / 0.2025
# Initial condition: v(0) = v0
v0 = 0.0 # Initial velocity value, change as needed
# Time points at which to solve for v (can be adjusted based on your requirements)
t_points = np.linspace(0, 10, 1000) # Adjust the time range as needed
# Solve the modified differential equation
v_values = odeint(model, v0, t_points)
# Calculate s values using cumulative sum of v values and corresponding time points
s_values = np.cumsum(v_values.flatten()) * (t_points[1] - t_points[0]) # Integration sum
# Calculate C values based on v values
C_values = []
for v in v_values:
v = v[0]
if 3300 * v < 10:
C = 322 / (3300 * v)
elif 10 < 3300 * v < 20000:
C = 10**(3.02 - 1.89 * np.log(3300 * v) + 0.411 * (np.log(3300 * v))**2 - 0.033 * (np.log(3300 * v))**3)
else:
C = 0 # Placeholder if conditions are not met
C_values.append(C)
# Plotting t vs C, t vs s, and t vs v
plt.figure(figsize=(12, 8))
plt.subplot(311)
plt.plot(t_points, C_values, label='C')
plt.xlabel('Time')
plt.ylabel('C')
plt.legend()
plt.subplot(312)
plt.plot(t_points, s_values, label='s')
plt.xlabel('Time')
plt.ylabel('s')
plt.legend()
plt.subplot(313)
plt.plot(t_points, v_values, label='v')
plt.xlabel('Time')
plt.ylabel('v')
plt.legend()
plt.tight_layout()
plt.show()
# Print the s values
print("s values:")
for s in s_values:
print(s)
```