Speed and Velocity Study Pack
Kibin's free study pack on Speed and Velocity includes a 5-section study guide, 25 quiz questions, 30 flashcards, and 5 open-ended Explain review questions. Sign up free to track your progress toward mastery, plus upload your own notes and recordings to create personalized study packs organized by course.
Last updated May 27, 2026
Speed and Velocity Study Guide
Master the distinction between speed and velocity — scalar vs. vector, distance vs. displacement, and why direction changes velocity even at constant speed. Covers average and instantaneous values, plus why net displacement determines whether average velocity is zero.
Key Takeaways
- •Speed is a scalar quantity measuring how fast an object moves, calculated as total distance divided by elapsed time, with no directional component.
- •Velocity is a vector quantity that combines speed with direction, calculated as displacement divided by elapsed time — making direction a mathematically essential part of the value.
- •Displacement and distance are distinct: displacement is the straight-line change in position from start to finish, while distance is the total path length traveled.
- •Average velocity can be zero even when an object has been moving, if the object returns to its starting position so that net displacement equals zero.
- •Instantaneous speed and instantaneous velocity describe motion at a single moment in time, found by shrinking the time interval of measurement toward zero.
- •A change in direction — even at constant speed — constitutes a change in velocity, because velocity depends on both magnitude and direction.
Distance and Displacement: Two Ways to Measure Position Change
Before defining speed or velocity, it is essential to distinguish between two different ways of quantifying how far something has moved, because each one pairs with a different motion descriptor.
Distance
- •Distance is the total length of the path an object actually travels, regardless of direction or starting point.
- •Distance is a scalar quantity — it has magnitude only and is always positive or zero.
- •Example: a runner who completes one full lap of a 400 m track has traveled a distance of 400 m.
Displacement
- •Displacement is the straight-line vector from an object's initial position to its final position, including direction.
- •Displacement can be positive, negative, or zero depending on the coordinate system chosen and the object's final location relative to its start.
- •Using the same runner: after one complete lap, displacement is 0 m because the runner ends exactly where they began.
Why the Distinction Matters
- •Speed is calculated using distance; velocity is calculated using displacement — so using the wrong quantity produces the wrong result.
- •Two objects can travel the same distance but have very different displacements if they move in different directions.
Speed: Magnitude of Motion Without Direction
Speed quantifies how fast an object moves through space, but it carries no information about which way that motion is directed.
Definition and Formula for Average Speed
- •Average speed equals total distance traveled divided by total elapsed time: speed = d / t.
- •The SI unit for speed is meters per second (m/s), though kilometers per hour (km/h) and miles per hour (mph) are also common.
- •Because distance is always non-negative and time is always positive, average speed is always a non-negative value.
Scalar Nature of Speed
- •Speed is a scalar quantity, meaning it is fully described by a single number and a unit — no direction is needed or included.
- •A car's speedometer reads speed, not velocity: it tells you how fast you are going but not which way.
Instantaneous Speed
- •Instantaneous speed is the speed of an object at one specific moment, equivalent to the magnitude of the instantaneous velocity at that moment.
- •Mathematically, instantaneous speed is the limit of average speed as the time interval approaches zero: |v| = lim(Δt→0) Δd/Δt.
- •On a distance-versus-time graph, instantaneous speed equals the absolute value of the slope of the tangent line at a given point.
Velocity: Speed Combined With Direction
Velocity is the vector counterpart to speed — it describes not just how fast an object moves but also the direction of that motion, making it a fundamentally richer and more precise physical quantity.
Definition and Formula for Average Velocity
- •Average velocity equals displacement divided by elapsed time: v̄ = Δx / Δt, where Δx is the change in position (final minus initial) and Δt is the time interval.
- •Because displacement is a vector, velocity is also a vector and must include a direction in its complete description.
- •Example: if a car moves 60 km north in 1 hour, its average velocity is 60 km/h north — the direction is inseparable from the value.
Sign Convention in One Dimension
- •In one-dimensional problems, direction is encoded using positive and negative signs relative to a chosen positive axis.
- •A velocity of +15 m/s and −15 m/s represent the same speed but opposite directions — these are physically distinct states of motion.
- •Choosing a consistent sign convention at the start of a problem prevents calculation errors when objects reverse direction.
When Average Velocity Equals Zero
- •If an object's net displacement over a time interval is zero — meaning it returns to its starting position — its average velocity is zero, even if it moved at high speed the entire time.
- •This is a key conceptual distinction: average speed for that same trip would be nonzero because distance traveled was nonzero.
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About this Study Pack
Created by Kibin to help students review key concepts, prepare for exams, and study more effectively. This Study Pack was checked for accuracy and curriculum alignment using authoritative educational sources. See sources below.
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Question 1 of 25
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A runner completes one full lap of a 400 m track. What is the runner's displacement at the end of the lap?
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Concept 1 of 5
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Scalars vs. Vectors
Explain the difference between a scalar quantity and a vector quantity in your own words. Why does this distinction matter when describing motion, and can you give an example of each from physics?
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