Quick Answer
Speed is a scalar — it tells you how fast something is moving (magnitude only). Velocity is a vector — it tells you how fast AND in what direction. A car going 60 mph has a speed of 60 mph. A car going 60 mph north has a velocity of 60 mph north.
Scalars vs. Vectors
To understand the difference, you first need to know the difference between a scalar and a vector.
A scalar is a quantity described by magnitude (size) only. Examples: temperature (72°F), mass (5 kg), distance (10 m).
A vector is a quantity described by both magnitude AND direction. Examples: displacement (10 m east), force (20 N downward), velocity (30 m/s north).
Speed is a scalar. Velocity is a vector. This is the core distinction.
| Feature | Speed | Velocity |
|---|---|---|
| Type of quantity | Scalar | Vector |
| Describes | How fast | How fast and in what direction |
| Based on | Distance | Displacement |
| Can be negative? | No | Yes |
| Example | 20 m/s | 20 m/s east |
Speed
Speed measures how fast an object is moving, with no regard for direction.
Average speed = total distance traveled / total time elapsed.
Units: m/s, km/h, mph — any distance unit per time unit.
Key point: speed is always non-negative. You cannot have a speed of −20 mph. A negative sign would imply direction, which makes it velocity, not speed.
Example: a runner completes a 400 m lap in 80 seconds. Average speed = 400 m / 80 s = 5 m/s.
Velocity
Velocity measures how fast an object is moving AND in which direction.
Average velocity = displacement / time elapsed.
Displacement is the straight-line distance from start to finish, with direction — not the total path length.
Units: same as speed, but with a direction: m/s north, km/h at 30° above horizontal, etc.
Key point: velocity can be negative. In one-dimensional motion, we pick a positive direction (usually right or up). Motion in the opposite direction has negative velocity.
Example: the same runner who ran a 400 m lap returns to the start. Displacement = 0 m. Average velocity = 0 m/s. Average speed = 5 m/s. These are different!
When Speed and Velocity Are Equal
Speed and the magnitude of velocity are always equal at any instant — this is called instantaneous speed vs. instantaneous velocity.
For average values, they are equal only when the object moves in a straight line in one direction the entire time (no backtracking, no turns).
As soon as the object changes direction, the total distance traveled exceeds the displacement, so average speed > |average velocity|.
Why This Matters for Physics Problems
Many SAT/ACT Physics questions test whether you can distinguish speed from velocity:
• "A car drives 60 km east, then 60 km west. What is the average velocity?" → Displacement = 0, so average velocity = 0.
• "What is the average speed?" → Total distance = 120 km, so average speed = 120 km / time.
Another common trap: an object moving in a circle at constant speed has changing velocity (because direction is always changing). This is why circular motion requires a net force (centripetal force) even at constant speed.
Worked Examples
Example 1
A car drives 100 km north in 2 hours, then 60 km south in 1 hour. Find (a) average speed and (b) average velocity.
Solution
- Total distance = 100 + 60 = 160 km.
- Total time = 2 + 1 = 3 hours.
- (a) Average speed = 160 km / 3 h ≈ 53.3 km/h.
- Displacement = 100 km north − 60 km south = 40 km north.
- (b) Average velocity = 40 km north / 3 h ≈ 13.3 km/h north.
Answer: (a) ≈ 53.3 km/h. (b) ≈ 13.3 km/h north.
Example 2
A ball is thrown upward at 15 m/s and caught at the same height 3 seconds later. What is the average velocity? Average speed?
Solution
- Displacement: the ball returns to the same height → displacement = 0 m.
- Average velocity = 0 m / 3 s = 0 m/s.
- The ball traveled up and then came back down. Total distance ≠ 0.
- Using kinematics: the ball rises for 1.5 s, falls for 1.5 s. Max height = (15)(1.5) − (1/2)(10)(1.5²) = 22.5 − 11.25 = 11.25 m.
- Total distance = 11.25 m up + 11.25 m down = 22.5 m.
- Average speed = 22.5 m / 3 s = 7.5 m/s.
Answer: Average velocity = 0 m/s. Average speed = 7.5 m/s.
Common Mistakes
Using "speed" and "velocity" interchangeably. In everyday language this is fine; in physics, they are different quantities with different formulas.
Using total distance instead of displacement when calculating velocity. Velocity uses displacement (start to finish, straight line with direction), not total path length.
Saying velocity cannot be zero. Velocity is zero whenever the object is momentarily at rest OR whenever displacement is zero over the time interval.
Forgetting that speed is always ≥ 0. If your calculation gives a negative speed, you have calculated velocity (or made an error).
Practice Problems
A cyclist rides 30 km east, then 30 km west, in 2 hours total. Find average speed and average velocity.
Hint: Total distance = 60 km. Displacement = 0 km.
A sprinter runs 100 m north in 10 s. What is the average speed? Average velocity?
Hint: Straight-line motion in one direction — are speed and velocity the same here?
An object moves at constant speed in a circle. Is its velocity constant? Explain.
Hint: Think about what changes as the object goes around the circle.
A car travels 80 km/h east for 1 hour, then 60 km/h west for 1 hour. Find average speed and average velocity.
Hint: Calculate total distance and displacement separately.
Frequently Asked Questions
Can speed and velocity be the same?
Yes. Average speed and the magnitude of average velocity are equal when an object travels in a straight line without changing direction. Instantaneous speed is always equal to the magnitude of instantaneous velocity.
Is speed equal to velocity?
Not always. Speed has magnitude only, while velocity includes both magnitude and direction. They have the same numerical magnitude only under certain motion conditions.
Can an object have constant speed but changing velocity?
Yes. In circular motion, an object can move at constant speed while its direction continually changes, so its velocity changes.
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