Kinematics and Dynamics

TL;DR

Kinematics describes how things move using concepts like displacement, velocity, and acceleration, without considering why. Dynamics, on the other hand, explains why things move the way they do by introducing forces and mass. Together, they form the foundation for understanding motion in the universe.

1. The Mental Model

Imagine you're watching a car. Kinematics is just describing its journey: how fast it's going, where it is, and if it's speeding up or slowing down. Dynamics is about why it's moving: the engine pushing it, the brakes stopping it, or gravity pulling it downhill.

2. The Core Material

When we talk about things moving, we first need to define a few concepts.

Displacement vs. Distance

Distance is the total path an object travels, regardless of direction. If you walk 5 meters north and then 5 meters south, you've covered a total distance of 10 meters. Displacement is the straight-line change in position from start to end, including direction. In that same example, if you end up back where you started, your displacement is 0 meters. Displacement is a vector quantity (has magnitude and direction), while distance is a scalar quantity (only magnitude).

Speed vs. Velocity

Similarly, speed is how fast an object is moving (rate of change of distance) and is a scalar. Velocity is how fast an object is moving in a specific direction (rate of change of displacement) and is a vector. Your speedometer shows speed. If you're told a plane is flying at 800 km/h east, that's its velocity.

$$
\text{Average Speed} = \frac{\text{Total Distance}}{\text{Total Time}}
$$

$$
\text{Average Velocity} = \frac{\text{Displacement}}{\text{Total Time}}
$$

Acceleration

Acceleration is the rate at which velocity changes. Since velocity is a vector, acceleration can happen in two ways: changing the object's speed, or changing its direction, or both. It's also a vector. If you're in a car and you hit the gas pedal, you accelerate. If you turn the steering wheel while maintaining the same speed, you're also accelerating because your direction is changing.

$$
\text{Acceleration} = \frac{\text{Change in Velocity}}{\text{Time}}
$$

Newton's Laws of Motion (Dynamics)

These three laws explain the relationship between force, mass, and motion.

Newton's First Law (Law of Inertia)

An object at rest stays at rest, and an object in motion stays in motion with the same speed an