Classical Mechanics · Motion & Description
Before equations, before calculus, before Newton — there is observation. How far? How fast? How quickly does fast change? Kinematics is the precise vocabulary for describing motion, and it is the gateway to all of classical mechanics.
Nature uses only the longest threads to weave her patterns, so each small piece of the fabric reveals the organization of the entire tapestry. The key is motion — and motion demands description before it demands explanation.
Idea 1 · Description of Motion
Kinematics describes how things move — not why. That distinction matters. Dynamics (Newton's Laws) explains causes. Kinematics gives us the language to describe any motion with precision before we ask what caused it.
Every description of motion begins with a reference point (origin) and a coordinate system. Once you fix those, three quantities fully describe the state of any moving object:
Speed is a scalar — it's just a number (how fast). Velocity is a vector — it has both magnitude and direction. This distinction matters enormously. A car at 60 mph going north and a car at 60 mph going south have the same speed but opposite velocities.
You walk 3 blocks east, then 3 blocks west. You've traveled a distance of 6 blocks. But your displacement is 0 — you're back where you started. Physics cares about displacement.
Average velocity = total displacement ÷ total time. Instantaneous velocity = velocity at one specific moment (what your car's speedometer shows).
Idea 2 · Constant Acceleration
When acceleration is constant (uniform), four equations connect position, velocity, acceleration, and time. You only need to know three of the five quantities to solve for the other two.
Final velocity = initial + (acceleration × time)
Position from initial spot, velocity, and acceleration
Velocity² connects to displacement — no time needed
Near Earth's surface, gravity pulls every object downward with the same acceleration: g = 9.8 m/s² (regardless of mass — Galileo proved this).
A ball dropped from rest:
All objects fall at the same rate — a feather and a hammer reach the same speed at the same time in a vacuum. The Moon is in free fall around Earth right now; it just also moves sideways fast enough to keep missing the ground.
Idea 3 · Projectile Motion
Feynman's key insight about projectile motion: the horizontal and vertical motions are completely independent. A bullet fired horizontally from a gun hits the ground at the same time as a bullet dropped straight down — both fall under the same gravitational acceleration.
Horizontal: no acceleration (ignoring air). Constant velocity.
Vertical: gravity acts. Uniformly accelerating.
For a given launch speed, the angle that maximizes horizontal range is 45°. At 45°, vertical and horizontal launch components are equal, creating the best balance between "going up long enough" and "moving forward fast enough."
A projectile's path is a perfect parabola (when air resistance is ignored). The landing speed equals the launch speed. The time going up equals the time coming down. The peak is exactly halfway along the range.
Idea 4 · The Calculus Connection
Newton and Leibniz formalized the idea — that velocity is the derivative of position with respect to time, and position is the integral of velocity. This was Newton's great invention: calculus born from motion.
On a position-time graph, the slope at any point is the instantaneous velocity. On a velocity-time graph, the area under the curve is the displacement.
Kinematics isn't just about physics — it's about how to read the world as a graph. Once you see that slope = rate of change and area = accumulation, you've understood the heart of calculus through motion.