Session 2: Rates of Change – Calculus in Motion

Discuss

How calculus models acceleration (e.g., takeoff speed). "Pilots feel it; designers predict it."

Code

import numpy as np
import matplotlib.pyplot as plt

t = np.linspace(0, 10, 100)
velocity = 10 * t - 0.5 * 9.81 * t**2  # Simple projectile velocity
accel = np.gradient(velocity, t)  # Derivative for acceleration

plt.plot(t, velocity, label='Velocity')
plt.plot(t, accel, label='Acceleration')
plt.xlabel('Time (s)')
plt.ylabel('Value (m/s or m/s²)')
plt.title('Rates of Change: Calculus in Flight')
plt.legend()
plt.grid(True)
plt.show()

Extend Session 1—use numpy to compute derivatives for velocity curves. Plot a simple parabolic flight path (like a thrown ball, bridging to baseball).

Excite

Animate the path with matplotlib—watch it "fly" on screen.

Homework

Add wind variable; observe path changes.