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Velocity vs Speed: What's the Difference?

Kinematics

Speed and velocity sound like the same thing, but in physics they are different quantities, and the difference matters. Speed tells you only how fast something is moving. Velocity tells you how fast and in which direction. That extra piece of information changes how the two are calculated, especially when an object turns around or returns to where it started.

Speed: how fast

Speed is a **scalar** quantity: it has a size but no direction. It is calculated as distance travelled divided by time taken, and its SI unit is the metre per second (m/s). A car's speedometer shows speed, it tells you how fast you are going, not where you are heading. Average speed uses the total distance covered, however winding the route was. A runner who covers 400 m in 80 s has an average speed of 5 m/s, regardless of the direction they ran in at any moment.

Velocity: how fast, and where to

Velocity is a **vector** quantity: it has both a size and a direction. It is calculated as displacement divided by time taken. **Displacement** is the straight-line distance from the start point to the end point, with direction, so it can be much smaller than the total distance travelled, or even zero. A runner who completes one lap of a 400 m track and returns to the start has zero displacement, so their average velocity over the lap is zero, even though their average speed was 5 m/s. The size of the velocity is sometimes called the speed, but the direction is what makes it velocity.

Instantaneous vs average

Both speed and velocity come in average and instantaneous forms. Average values cover a whole journey, while instantaneous values describe a single moment, what the speedometer shows right now, or the velocity at one point on a curve. For an object moving in a straight line at a constant speed, average and instantaneous values are the same. When motion changes, they differ: a car that speeds up and slows down in traffic has a constantly changing instantaneous velocity, but only one average velocity for the whole trip. In equations of motion, v usually means instantaneous velocity at a particular time.

Common mistakes

• Using speed and velocity as if they were the same. Correction: speed is a scalar (size only); velocity is a vector (size and direction).
• Using total distance when calculating velocity. Correction: velocity uses displacement, the straight-line change in position, not the distance travelled.
• Thinking zero average velocity means the object never moved. Correction: it only means the object ended where it started; it may have moved a long way in between.

Practice questions

1. A car travels 120 km in 2 hours. What is its average speed?
   Show answer

   Average speed = 120 km / 2 h = 60 km/h.

2. A cyclist rides 10 km east, then 10 km west back to the start, in 1 hour. What is the average velocity?
   Show answer

   Displacement is 0 km, so average velocity = 0 km/h, even though the average speed was 20 km/h.

3. A ball is thrown straight up at 15 m/s. What is its velocity at the top of its flight?
   Show answer

   0 m/s at the top, it momentarily stops before falling back down, though its acceleration is still 9.81 m/s² downward.

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