Can velocity be negative?

Yes. Because velocity is a vector, it uses positive and negative signs to indicate direction. If we decide that moving right is positive, then a negative velocity simply means the object is moving to the left.

Can average speed be zero while average velocity is not?

No. If your average speed is zero, it means you have covered zero distance over a period of time, meaning you never moved. If you never moved, your displacement is zero, so your average velocity must also be zero.

Does a car speedometer show average or instantaneous speed?

A car speedometer shows instantaneous speed. It tells you exactly how fast you are moving at that specific fraction of a second, not your average speed over the whole trip.

What is the difference between speed and velocity?

Speed is simply a measure of how fast an object is moving. When you look at the speedometer in a car, it tells you your speed, like 60 miles per hour, but it does not care where you are going. Velocity, on the other hand, is speed with a specific direction. If you are driving 60 miles per hour straight north, that complete description is your velocity. Think of speed as the effort you are putting into running, and velocity as your actual progress toward a finish line. If you run in circles at top speed, you are certainly moving fast, but your overall velocity might be zero because you are not getting anywhere new. In physics, keeping track of direction is crucial, which is why velocity is usually the more useful tool.

Scalars vs. Vectors

The fundamental difference between speed and velocity comes down to how we categorize measurements in physics. Speed is a scalar quantity. Scalars only have a magnitude (a size or number) and no direction. Other examples of scalars include temperature and mass. Velocity is a vector quantity. Vectors have both a magnitude and a direction. To fully describe a vector, you must state which way it points. In one-dimensional kinematics, we often use positive and negative signs to represent this direction, such as $+50$ m/s for moving right and $-50$ m/s for moving left.

Distance vs. Displacement

To calculate average speed, you divide the total distance traveled by the time it took. Distance is the total length of the path you actually walked or drove, regardless of twists and turns. To calculate average velocity, you divide displacement by time. Displacement is the straight-line distance from your starting point to your ending point, including the direction. Because velocity relies on displacement, a journey that ends exactly where it started will have an average velocity of zero, no matter how much distance was covered.

Where Students Slip Up

A very common trap is assuming that average speed and average velocity are just different words for the same number. For a one-way trip in a perfectly straight line without turning back, their magnitudes (the numbers) are indeed the same. However, if an object changes direction at any point, the distance will become larger than the displacement. When this happens, the average speed will be greater than the magnitude of the average velocity. Always ask yourself if the object turned around before you assume speed equals velocity.

Worked through

A cyclist rides 40 kilometers due East in 2 hours. She then turns around and rides 10 kilometers due West in 1 hour. Calculate her average speed and her average velocity for the entire trip.

First, let us find the average speed. The total distance traveled is 40 km + 10 km = 50 km. The total time taken is 2 hours + 1 hour = 3 hours. Average speed = total distance / total time = 50 / 3 = 16.67 km/hr. Next, let us find the average velocity. We must calculate the displacement. If East is positive, her displacement is +40 km (East) and then -10 km (West), giving a total displacement of +30 km. The total time is still 3 hours. Average velocity = displacement / total time = 30 / 3 = +10 km/hr. Her average velocity is 10 km/hr East.

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Where this comes from: OpenStax College Physics, Chapter 2: Kinematics · Khan Academy: One-dimensional motion Unit