Introduction: Describing Motion
Kinematics is the study of motion. Before we dig into why things move (that's dynamics, which we'll cover later), we need to nail down how to describe motion with precision.
"The car moved fast" or "I walked a long way" might work in conversation, but physics needs more. Did the car move toward you or away? Did you end up where you started? These details completely change what happened.
This section builds a precise vocabulary for motion around two core questions:
- Where is the object? (Position)
- How fast is its position changing? (Velocity)
You'll see why direction matters and how to read position-time graphs, which turn out to be one of the most useful tools in all of physics.
Position
To describe where an object is, we need a coordinate system. For 1D kinematics, we'll use a number line with an origin , a positive direction (usually right), and a negative direction (usually left).
Position is your location on this axis, written as a signed number with units. The sign indicates which side of the origin you're on.
Position (x) = +3.0 m
Drag the marker to change position
Check Your Understanding
A basketball player is standing at x = -7 m on the court. Which statement is correct?
Displacement & Distance
- Δx= Displacement (vector)
- x f= Final Position
- x i= Initial Position
- | d |= Distance (scalar, total path length)
- Σ = Sum of all terms (sigma notation)
- Δx n= Displacement for the n-th segment
- |Δx| = Magnitude of displacement for each segment (always positive)
Displacement (
Distance (
The key difference: Walk in a circle back to where you started? Your displacement is zero (you ended where you began), but your distance definitely isn't (you traveled the entire circumference).
Consider another example: you move from position 2 m to position 7 m, then back to position 5 m.
- Displacement: Δx= 5 m - 2 m = +3 m (straight-line change from start to finish)
- Distance: | d |= |2→7| + |7→5| = 5 m + 2 m = 7 m (total path traveled)
Try it yourself in the interactive visualization below. Drag the markers to see how displacement and distance differ as you create different paths.
Displacement
Distance Traveled
Drag the markers to see how displacement and distance traveled differ
Check Your Understanding
A student walks from x = 2m to x = 8m, then back to x = 5m. What is their total distance? What is their displacement?
Velocity
Velocity measures how fast position changes. It's displacement over a time interval.
- v avg= Average Velocity
- Δx= Displacement
- Δt= Time Elapsed
Average Velocity
Average Speed
Click and drag to define motion—faster dragging creates larger velocity
Remember: Velocity is a vector, so the sign matters. Positive means moving in the positive direction, negative means the opposite.
Check Your Understanding
An object moves from x = 10m to x = 2m in 4 seconds. What is its average velocity? What does the sign tell you about its motion?
Instantaneous Velocity
Average velocity gives you the big picture over an interval. instantaneous velocity tells you your velocity at a single instant in time.
Think about a car's speedometer. When it reads 60 mph, that's your instantaneous velocity right now, not your average for the whole trip.
From Average to Instantaneous
As the time interval approaches zero, average velocity approaches instantaneous velocity.
Shrink
Why It Matters
Most real motion involves changing velocity. Average velocity over a long interval doesn't tell you what's happening moment to moment. In the next section, you'll see how position-time graphs make this visual: instantaneous velocity is the slope at a point.
Check Your Understanding
A car's speedometer reads 50 mph at a specific moment. Which statement is correct?