Difficulty: Introductory | Prerequisites: Basic algebra and an intuitive sense of what "force" and "speed" mean. No prior physics coursework required.
Mechanics is the oldest and most foundational branch of physics. It sits at the start of nearly every general physics sequence because everything that follows (thermodynamics, electromagnetism, waves) builds on its language of forces, energy and motion. If you can describe how and why objects move, you have the toolkit for the rest of the course. The material here introduces the two main sub-branches, kinematics and dynamics, and shows how they divide the same physical situation into "what is happening" and "why it is happening."
Mechanics is the study of motion and the forces that cause it. It splits into kinematics (describing motion with displacement, velocity and acceleration) and dynamics (explaining motion through forces, energy and Newton's laws). Everything from car braking distances to satellite orbits falls under mechanics.
Mechanics
The branch of physics concerned with the motion of objects and the forces that produce or change that motion.
In simple terms, mechanics answers two questions: how does something move, and what made it move?
Kinematics
The sub-branch of mechanics that describes motion using displacement, velocity and acceleration, without reference to the forces involved.
Think of it as the "what is happening" side of motion: position, speed, direction and how they change over time.
Dynamics
The sub-branch of mechanics that explains motion by analysing the forces acting on objects, using concepts such as Newton's laws, work, energy and power.
Think of it as the "why it is happening" side: what pushes, pulls, speeds up or slows down the object.
Displacement
The change in an object's position, described as a vector (magnitude and direction) from the starting point to the ending point.
In simple terms, displacement is how far you ended up from where you started, and in which direction, regardless of the path you took.
Velocity
The rate of change of displacement with respect to time, expressed as a vector.
In simple terms, velocity tells you how fast something is moving and in which direction.
Acceleration
The rate of change of velocity with respect to time.
In simple terms, acceleration is how quickly something is speeding up, slowing down, or changing direction.
Deals with the geometry of motion: where an object is, how fast it is going, whether it is speeding up or slowing down.
Key quantities: displacement, velocity, acceleration.
Does not ask why the object moves. A kinematics problem gives you positions and times and asks you to find speeds or accelerations (or vice versa).
Example: a car on a straight road. Kinematics lets you state that the car is at position x = 50 m, travelling at 20 m/s, accelerating at 2 m/s². It says nothing about the engine, the brakes or air resistance.
Deals with the causes of motion: forces, and the relationship between force and acceleration.
Central framework: Newton's three laws of motion.
First law (inertia): an object stays at rest or in uniform motion unless acted on by a net force.
Second law: F = ma. Net force equals mass times acceleration.
Third law: every action has an equal and opposite reaction.
Related energy concepts: work, kinetic energy, potential energy, power.
Example (same car): dynamics identifies the engine force pushing the car forward, air resistance and friction opposing the motion, and the brake force when the car slows. These forces, combined through F = ma, explain the acceleration kinematics measured.
Kinematics gives you the mathematical description of motion.
Dynamics gives you the physical explanation for that motion.
A complete mechanics problem typically uses both: dynamics to find accelerations from forces, kinematics to turn those accelerations into positions and velocities over time.
v = v_0 + atVelocity after time t, starting from initial velocity v₀ with constant acceleration a.
x = x_0 + v_0 t + \frac{1}{2}at^2Position after time t under constant acceleration.
v^2 = v_0^2 + 2a(x - x_0)Relates velocity to displacement without needing time.
F_{\text{net}} = maNewton's second law: net force equals mass times acceleration. This is the bridge between kinematics (the a) and dynamics (the F).
Engineers use kinematics and dynamics every time they design a vehicle, a bridge, or a machine. A car's braking distance is a kinematics calculation; the brake pad material and calliper force are dynamics. Structural engineers apply Newton's laws to ensure buildings and bridges can handle wind loads and earthquakes. Aerospace engineers use the same principles to plot satellite orbits and calculate the thrust a rocket needs to reach orbit.
Students often confuse speed and velocity. Speed is a scalar (magnitude only); velocity is a vector (magnitude and direction). An object moving in a circle at constant speed has changing velocity because its direction is changing.
Students often think that if an object is not moving, no forces act on it. Forces can be present and balanced (net force = zero). A book on a table has gravity pulling it down and the table pushing it up.
Students often treat kinematics and dynamics as separate subjects. They are two lenses on the same situation. A problem that asks "how far does the car travel before stopping" typically requires both.
Students often assume acceleration means "speeding up." Acceleration is any change in velocity, including slowing down (sometimes called deceleration) and changing direction.
Expect to be asked to classify a problem as kinematics or dynamics (or both). Know which quantities belong to which branch.
Newton's second law (F = ma) is the single most-tested equation in introductory mechanics. Be comfortable rearranging it and identifying all forces on an object.
Free-body diagrams are the standard tool for dynamics problems. Practice drawing them: one dot for the object, one arrow per force, labelled with magnitude and direction.
Problems that combine kinematics equations with F = ma appear on nearly every introductory physics exam. The typical pattern: use dynamics to find acceleration, then plug it into a kinematics equation to find distance or time.
True or false: Kinematics is concerned with the forces that cause motion. (False. Kinematics describes motion without reference to forces.)
Fill in the blank: Newton's second law states that net force equals ______ times ______. (mass, acceleration)
True or false: An object moving at constant speed in a circle has zero acceleration. (False. Its direction is changing, so its velocity is changing, which means it is accelerating.)
Fill in the blank: The two main branches of mechanics are ______ and ______. (kinematics, dynamics)
True or false: Displacement and distance are the same quantity. (False. Displacement is a vector from start to finish; distance is the total length of the path travelled.)
Q: A car accelerates uniformly from rest at 3 m/s² for 5 seconds. What is its final velocity?
A: Using v = v₀ + at, with v₀ = 0, a = 3 m/s² and t = 5 s: v = 0 + (3)(5) = 15 m/s.
Q: Define kinematics and dynamics in one sentence each.
A: Kinematics is the description of motion (position, velocity, acceleration) without reference to forces. Dynamics is the study of the forces that cause or change motion.
Q: A 10 kg box sits on a frictionless surface. You push it with a horizontal force of 20 N. What is its acceleration?
A: From F = ma, a = F/m = 20 N / 10 kg = 2 m/s².
Q: Why is velocity a vector but speed a scalar?
A: Velocity includes both magnitude and direction (e.g. 5 m/s north). Speed is only the magnitude (5 m/s), with no directional information.
Q: A ball is thrown straight up. At the very top of its arc, is its acceleration zero?
A: No. Its velocity is momentarily zero, but gravity still acts on it, so its acceleration is 9.8 m/s² downward throughout the flight.
Mechanics leads directly into energy and momentum (later chapters in most general physics courses), where the same forces reappear but are analysed through conservation laws rather than F = ma alone. It also underpins circular motion and gravitation: planetary orbits are a dynamics problem with gravity as the force and elliptical kinematics as the description. If you go on to study waves or thermodynamics, you will find that the language of displacement, force and energy carries over almost unchanged.
Mechanics, classical mechanics, Newtonian mechanics, kinematics, dynamics, motion, force, Newton's laws, displacement, velocity, acceleration, speed, inertia, F = ma, free-body diagram, net force, work, energy, power, general physics, introductory physics, University of Washington, PHYS 121