Feynman on Acceleration

In earlier chapters of his Lectures on Physics, Richard Feynman explored motion in terms of distance and velocity. We learned that velocity is the rate at which distance changes - in other words, how fast and in what direction an object is moving. But Feynman now takes us a step deeper: instead of asking how far or how fast, he asks, how does the speed itself change over time? This is the idea of acceleration.

From cars to falling bodies

Feynman begins with a familiar comparison: a car that boasts about going from zero to sixty in ten seconds. That gives us a sense of average speed change, but what if we want to know the change at every instant? That’s what acceleration measures: how quickly velocity itself is shifting, second by second.

To make this concrete, he turns to the simplest case - a freely falling object. We already know that, in such motion, velocity increases steadily as time goes on. By looking at how much the velocity grows each second, we discover that the increase is the same each time interval. In other words, the acceleration is constant. For falling objects near the Earth’s surface, this constant value tells us how much speed is gained every second.

Why is it constant?

The constancy isn’t an accident. According to Newton’s laws, the rate of change of velocity depends directly on the force applied. Since gravity provides a steady pull downward, the resulting acceleration is equally steady.

In other motions, where forces vary, acceleration won’t be so simple - it may grow, shrink, or even change direction as time passes. But the falling-body example serves as a clean entry point into the concept.

Peeling layers with derivatives

Feynman builds a chain of reasoning:

  1. Distance tells us where an object is.
  2. The rate at which distance changes gives us velocity.
  3. The rate at which velocity changes gives us acceleration.

Each step involves looking one level deeper into how quantities evolve over time. And just as velocity can be found from distance, acceleration can also be worked backward: if we know the acceleration, we can recover velocity and distance by a process called integration.

Motion in more than one direction

So far, the story has been about straight-line motion. But life rarely moves in one dimension, and Feynman widens the view to two and three dimensions.

He sets up a grid - an x-axis and a y-axis - to keep track of position in a plane. At any moment, an object has both an x-distance and a y-distance. Velocity, then, must also be split into components: one part along x, one part along y. The same goes for acceleration.

To get the actual speed and direction, we combine these components. Imagine breaking a step into a horizontal stride and a vertical stride, then using geometry to find the true diagonal path. That’s what happens when velocity or acceleration is pieced together from components.

The beauty of compound motion

Feynman finishes with a classic example: a ball thrown forward while gravity pulls it down. Horizontally, it keeps a steady pace. Vertically, its downward speed increases steadily because of constant acceleration. Put these two motions together, and the ball traces a curve. When you plot that curve, it turns out to be a parabola.

This isn’t just a textbook abstraction - it’s the path of every tossed ball, every spray of water from a hose, every projectile under Earth’s gravity. What looks like graceful arc in the air is, at heart, the simple marriage of steady horizontal motion with steady vertical acceleration.

Stepping back

In this chapter, Feynman isn’t just defining acceleration; he’s weaving it into the hierarchy of motion. Distance leads to velocity, velocity leads to acceleration, and with those three ideas - plus Newton’s law connecting force and acceleration - the groundwork is laid for nearly all of mechanics.

The chapter’s takeaway is simple but profound: acceleration is not an afterthought, but the natural next step in understanding motion. Once you grasp how velocities change, the world’s curves and arcs fall neatly into place.

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