Distinction Between Speed and Velocity: Speed Is a Scalar Based on Distance, and Velocity Is a Vector Based on Displacement
The distinction between speed and velocity is that speed is a scalar quantity that measures distance per unit time, and velocity is a vector quantity that measures displacement per unit time. Velocity includes direction, and speed does not. This article covers definitions, 8 differences, formulas, units, graphs, and 7 worked examples.
What Is the Distinction Between Speed and Velocity?
Speed measures how fast an object moves, and velocity measures how fast and in which direction an object moves. According to OpenStax University Physics, speed has no direction, so speed is a scalar. Velocity is a vector with magnitude and direction.
The table below lists 8 differences between speed and velocity.
| No. | Property | Speed | Velocity |
|---|---|---|---|
| 1 | Quantity type | Scalar | Vector |
| 2 | Measures | Rate of change of distance | Rate of change of position (displacement) |
| 3 | Direction | Not included | Included |
| 4 | Average equation | Total distance / elapsed time | Displacement / elapsed time |
| 5 | Instantaneous equation | Magnitude of instantaneous velocity, |v| | dx/dt |
| 6 | Possible values | Zero or positive | Positive, negative, or zero |
| 7 | Value for a round trip | Positive | Zero |
| 8 | Effect of a direction change at constant speed | Speed stays the same | Velocity changes |
What Is Speed?
Speed is the distance traveled per unit time. Speed is a scalar because it has magnitude and no direction, according to OpenStax Physics. Scalar quantities include distance, speed, time, mass, and energy.
Average speed equals total distance divided by elapsed time. Instantaneous speed equals the magnitude of the instantaneous velocity, as stated in OpenStax University Physics.
OpenStax describes a 30-minute round trip with a total distance of 6 km. The average speed for that trip is 12 km/h.
What Is Velocity?
Velocity is the rate of change of position, and it includes direction. The average velocity equation is v = Δx / Δt, where Δx is displacement and Δt is elapsed time. OpenStax University Physics defines average velocity as total displacement divided by the time needed for that displacement.
Instantaneous velocity is the limit of average velocity as the time interval approaches zero, written v = dx/dt. A velocity of 15 m/s east has a magnitude of 15 m/s and an eastward direction.
What Are the Formulas for Speed and Velocity?
The formula for average speed is s = d / t, and the formula for average velocity is v = Δx / Δt. The table below lists 4 formulas for speed and velocity.
| Quantity | Equation | Description |
|---|---|---|
| Average speed | s = d / t | Total distance divided by elapsed time |
| Average velocity | v = Δx / Δt | Displacement divided by elapsed time |
| Instantaneous speed | s = |v(t)| | Magnitude of the instantaneous velocity |
| Instantaneous velocity | v = dx/dt | Derivative of position with respect to time |
The list below defines the symbols in the table.
- s: speed (m/s)
- v: velocity (m/s)
- d: distance traveled (m)
- Δx: displacement (m)
- t, Δt: time and elapsed time (s)
- x: position (m)
What Is the Difference Between Distance and Displacement?
Distance is the total length of the path traveled, and displacement is the straight-line change in position from start to end. Distance is a scalar, and displacement is a vector. Speed uses distance, and velocity uses displacement.
A walk of 3 m east followed by 4 m north has a distance of 7 m. The displacement is 5 m at an angle of 53° north of east. The path takes 7 s, so the average speed is 1 m/s and the average velocity is 0.71 m/s at 53° north of east.
When Are Speed and Velocity Equal in Magnitude?
Speed equals the magnitude of velocity when an object moves in a straight line without reversing direction. In that case, distance equals the magnitude of displacement. OpenStax states that average speed is not necessarily equal to the magnitude of average velocity.
Average speed is greater than or equal to the magnitude of average velocity, because distance is greater than or equal to the magnitude of displacement.
What Are Examples of Speed and Velocity Calculations?
The table below shows 7 worked examples. Each row lists the scenario, known values, speed result, and velocity result.
| No. | Scenario | Known Values | Speed Result | Velocity Result |
|---|---|---|---|---|
| 1 | Round trip to a store | Distance 6 km, time 0.5 h, displacement 0 km | 12 km/h | 0 km/h |
| 2 | One lap on a 400 m track | Distance 400 m, time 80 s, displacement 0 m | 5 m/s | 0 m/s |
| 3 | Walk 3 m east, then 4 m north | Distance 7 m, displacement 5 m, time 7 s | 1 m/s | 0.71 m/s at 53° north of east |
| 4 | Straight run east | Distance 100 m, time 10 s | 10 m/s | 10 m/s east |
| 5 | Two particles moving in opposite directions | Velocities +10 m/s and -10 m/s | 10 m/s for each particle | +10 m/s and -10 m/s |
| 6 | Uniform circular motion | Radius 0.5 m, period 2 s | 1.57 m/s | Changes direction continuously, 0 m/s average over 1 revolution |
| 7 | Position function x(t) = 3t² – 12t at t = 1 s | v(t) = 6t – 12 | 6 m/s | -6 m/s |
How Do Speed and Velocity Differ on a Graph?
The slope of a position-time graph shows velocity, according to the OpenStax University Physics summary. The list below summarizes 4 graph relationships.
- Slope of a position-time graph represents velocity.
- Negative slope on a position-time graph represents negative velocity.
- Absolute value of the slope represents speed.
- Slope of a distance-time graph represents speed.
What Are the Units of Speed and Velocity?
The SI unit of both speed and velocity is meters per second (m/s). Velocity adds a direction to the unit, such as 20 m/s north. The table below converts common units to m/s.
| Unit | Symbol | Equivalent in m/s |
|---|---|---|
| Meter per second | m/s | 1 |
| Kilometer per hour | km/h | 0.2778 |
| Mile per hour | mph | 0.4470 |
| Foot per second | ft/s | 0.3048 |
| Knot | kn | 0.5144 |
Which Instruments Measure Speed and Velocity?
Speedometers measure speed, and velocity measurement requires both speed and direction. Three instruments illustrate the difference:
- Speedometers: display the instantaneous speed of a vehicle
- Odometers: record the total distance traveled
- GPS receivers: calculate velocity from changes in position over time
How Do Speed, Velocity, and Acceleration Relate?
Acceleration is the rate of change of velocity, so a change in speed or a change in direction produces acceleration. An object in uniform circular motion has constant speed and a changing velocity direction. OpenStax Physics states that this object is always accelerating.
What Are Common Misconceptions About Speed and Velocity?
Four misconceptions occur most often.
- Using speed and velocity as synonyms: physics assigns speed to distance and velocity to displacement and direction.
- Assuming average speed equals the magnitude of average velocity: the 2 values differ whenever the path is not a straight line in one direction.
- Assuming constant speed means constant velocity: a change in direction changes velocity.
- Treating negative velocity as slower motion: the negative sign indicates direction, and speed is the absolute value.
Where Do Speed and Velocity Apply in Real Life?
Speed and velocity apply to 5 main fields.
- Transportation: speed limits use speed, such as 100 km/h, and navigation uses velocity, which combines speed and heading
- Aviation: flight planning uses velocity to account for aircraft speed and heading
- Meteorology: wind reports give wind speed and wind direction, which together define wind velocity
- Sports science: sprint analysis uses speed, and ball tracking uses velocity
- Spaceflight: the International Space Station travels at about 7.9 km/s, according to ScienceABC, and its velocity direction changes continuously along the orbit
What Do People Also Ask About Speed and Velocity?
What is the main difference between speed and velocity?
Speed is a scalar that has magnitude only, and velocity is a vector that has magnitude and direction.
Is velocity speed with direction?
Yes, instantaneous velocity is instantaneous speed combined with a direction.
Can speed be negative?
No, speed is zero or positive because speed has no direction.
Can velocity be negative?
Yes, negative velocity indicates motion opposite to the chosen positive direction.
Can an object have constant speed and changing velocity?
Yes, velocity changes if direction changes, as in uniform circular motion.
Can average velocity be zero while average speed is not zero?
Yes, a round trip has zero displacement and a positive distance.
What is the formula for speed?
The formula for average speed is s = d / t.
What is the formula for velocity?
The formula for average velocity is v = Δx / Δt.
What are the units of speed and velocity?
The SI unit of speed and velocity is meters per second (m/s).
Is average speed greater than the magnitude of average velocity?
Average speed is greater than or equal to the magnitude of average velocity, because distance is greater than or equal to the magnitude of displacement.
What Is the Distinction Between Speed and Velocity in Summary?
The distinction between speed and velocity is speed is a scalar based on distance, and velocity is a vector based on displacement. Both quantities use the SI unit m/s. Velocity includes direction and can be negative. Speed excludes direction and is zero or positive. A round trip gives a positive average speed and a zero average velocity. A direction change at constant speed changes velocity.
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