Displacement and Velocity
Displacement, velocity, and acceleration form the vocabulary of kinematics: displacement vs. distance, speed vs. velocity, and rate of change of velocity.
Building on the vector/scalar distinction, three quantity pairs form the vocabulary of kinematics: displacement vs. distance, speed vs. velocity, and acceleration.
Key Takeaways
Displacement (vector) is the straight-line change in position with direction; distance (scalar) is the total path length traveled.
Velocity (vector, Δx/Δt) includes direction; speed (scalar, distance/Δt) does not.
Acceleration (vector, a = Δv/Δt) measures the rate of change of velocity — and can occur from a change in speed, direction, or both.
Displacement vs. Distance
Displacement (Δx) is the change in position of an object, measured in a straight line from the initial position (xi) to the final position (xf). It's a vector quantity — it has both magnitude and direction, telling you "how far" and "in what direction" an object has moved from its starting point.
Distance, in contrast, is the total path traveled by an object, regardless of direction. It's a scalar quantity — it has magnitude only, adding up every step taken along the way.
For example, if you walk 10 meters east, then 10 meters west, your total distance traveled is 20 meters — but your displacement is zero, because you end up exactly where you started.
Displacement | Distance | |
|---|---|---|
Quantity type | Vector | Scalar |
Measures | Straight-line change in position, with direction | Total path length traveled |
Walk 10 m east, then 10 m west | 0 m | 20 m |
While displacement measures the shortest route between two points, distance measures the entire route traveled.
Speed vs. Velocity
Velocity is a vector quantity representing the rate of change of displacement over time — it tells you not just how fast an object is moving, but in which direction:
Average Velocity = Δx / Δt
where Δx is the displacement and Δt is the time interval over which it occurs. The units for velocity are meters per second (m/s). For example, driving 100 kilometers north in 2 hours gives a velocity of 50 km/h north; driving the same distance south in the same time gives a velocity of 50 km/h south — same speed, opposite velocity.
Speed, by contrast, is a scalar quantity: it measures how fast an object is moving without considering direction, calculated by dividing total distance by total time:
Speed = Distance / Δt
Since speed doesn't account for direction, it only tells you "how fast" — whether you're moving north or south at 50 km/h, your speed is the same either way.
Velocity | Speed | |
|---|---|---|
Quantity type | Vector | Scalar |
Formula | Δx / Δt | Distance / Δt |
Tells you | How fast, and in which direction | How fast only |
Acceleration
Acceleration (a) is a vector quantity representing the rate of change of velocity over time — it describes how quickly an object is speeding up, slowing down, or changing direction:
a = Δv / Δt
where Δv is the change in velocity and Δt is the time interval over which that change occurs. The units for acceleration are meters per second squared (m/s²).
MCAT Callout — Acceleration Isn't Just About Speeding Up: Because velocity is a vector, a change in direction counts as acceleration even if speed stays constant. When a car rounds a corner at a constant speed, it's still accelerating — its direction (and therefore its velocity) is continuously changing.
Common MCAT Mistakes
Treating "distance" and "displacement" as interchangeable. Distance is the total path length (scalar); displacement is the straight-line change in position (vector). A round trip has nonzero distance but zero displacement.
Confusing speed with velocity on direction-dependent questions. Speed only tells you magnitude; if a question asks about direction or a sign change, you need velocity, not speed.
Assuming acceleration means "speeding up." Constant-speed circular or curved motion still has acceleration, because the direction of velocity is changing.
Mixing up the numerator in the velocity and speed formulas. Velocity uses displacement (Δx) in the numerator; speed uses total distance. Swapping them gives the wrong quantity, especially on round-trip problems.
MCAT-Style Concept Check
Question: A runner sprints 400 meters around a circular track, finishing back at the starting point, in a time of 50 seconds. What is the runner's average velocity?
A) 8 m/s
B) 0 m/s
C) 400 m/s
D) 50 m/s
Answer: B
Explanation: Average velocity equals displacement divided by time (Δx/Δt). Because the runner finishes at the same point where they started, the displacement is 0 meters, regardless of the 400-meter path length actually run. So average velocity is 0 m/s. (Average speed, by contrast, would be 400 m / 50 s = 8 m/s — option A — since speed uses total distance, not displacement.)
FAQ
What's the difference between displacement and distance?
Displacement is the straight-line change in position from start to finish, including direction — it's a vector. Distance is the total length of the path actually traveled, with no regard for direction — it's a scalar. They're only equal when motion is in a single direction with no backtracking.
Why can velocity be zero even if an object is moving?
Average velocity depends only on the net displacement over a time interval. If an object returns to its starting position (like a runner finishing a lap), the displacement — and therefore the average velocity — is zero, even though the object covered real distance and had nonzero speed throughout.
Is acceleration only about speeding up or slowing down?
No. Acceleration is the rate of change of velocity, and velocity includes direction. An object moving at constant speed but changing direction — like a car turning a corner — is still accelerating, because its velocity vector is changing.
What are the units for velocity and acceleration?
Velocity is measured in meters per second (m/s), the same units as speed. Acceleration is measured in meters per second squared (m/s²), since it's the rate of change of velocity over time.
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