Equations of Motion for Freely Falling Bodies

📚 Key Concepts

🔹 Real-Life Example: Throwing a Ball or Bungee Jumping

When you throw a ball upward, it slows down due to gravity, stops momentarily at its maximum height, and then falls back down with increasing speed. Similarly, a bungee jumper experiences free fall until the rope pulls them back. These motions follow the equations of motion, making them predictable and measurable.

🔹 Equations of Motion: Mathematical relationships between displacement, velocity, acceleration, and time for objects moving with uniform acceleration.

🧪 Important Formulas

🔸 The Three Kinematic Equations (Using g for Gravity)

First Equation: v = u + gt
Relates final velocity (v), initial velocity (u), acceleration due to gravity (g), and time (t)
Second Equation: s = ut + ½gt²
Relates displacement (s), initial velocity (u), acceleration (g), and time (t)
Third Equation: v² = u² + 2gs
Relates final velocity (v), initial velocity (u), acceleration (g), and displacement (s)

🔹 Variables Explained

u: Initial velocity (m/s)
v: Final velocity (m/s)
g: Acceleration due to gravity (9.8 m/s²)
t: Time (seconds)
s: Displacement (meters)

🔹 Sign Convention for Direction

Upward motion: Positive (+)
Downward motion: Negative (–)
Use g = –9.8 m/s² for upward motion
Use g = +9.8 m/s² for downward motion

🔍 Advanced: Negative Acceleration in Upward Motion

When an object is thrown upward, gravity pulls it downward, acting against its motion. This causes the object to decelerate (negative acceleration). At the highest point, its velocity becomes zero before it starts falling back down with increasing speed.