# Speed

Speed is a measurement of how fast an object moves. In everyday use, "speed" is typically used to describe average speed, which is the distance an object travels over a period of time.

When talking about speed in the context of physics, it is important to distinguish between average speed and instantaneous speed. As mentioned, average speed is distance traveled over a period of time. On the other hand, instantaneous speed is the speed of an object at a specific (very short) moment in time. The shorter the time period, the more accurate the instantaneous speed.

As a comparison, imagine that you could travel at exactly 45 miles per hour (mph) for 1 hour. In such a case, you would travel 45 miles over the period of 1 hour. At any point during that trip, your instantaneous speed is 45 mph. Your average speed over that period of time would also be 45 mph.

However, it is also possible to travel 45 miles in 1 hour while traveling at different speeds. If you drove at exactly 30 mph for 20 minutes, you would cover a distance of 10 miles. If you then drove 52.5 mph for the remaining 40 minutes, you would still have covered 45 miles over the period of one hour, and your average speed would be 45 mph. However, depending whether you measure your speed during the first 20 minutes or the latter 40 minutes, your instantaneous speed would be either 30 mph or 52.5 mph, respectively.

## Units of speed

The unit of speed used in the International System of Units (SI) is the meter per second (m/s). It is an SI derived unit of speed. Two other units of speed that are more commonly used in everyday life are the mile per hour (mph) and kilometer per hour (km/h). Kilometers per hour is the most commonly used unit of speed for traffic purposes and on speedometers. In the United States, miles per hour is a more commonly used unit for these purposes, but it is not uncommon for speedometers to show both mph and km/h.

The above are all measurements of land speed. For air and marine travel, knots (kn) is used instead.

## Speed vs velocity

While speed and velocity are terms that are frequently used interchangeably, in the context of physics, they have separate definitions. Speed is a scalar value, and has no direction. Velocity on the other hand, does have a direction. This is the key difference between the two.

If we know how fast an object is moving, and in what direction, then we know its velocity. If we only know how fast the object is moving, but not its direction, then we know its speed. For example, if Jordan travels at a speed of 50 miles per hour and uses his compass to ensure that he travels exactly north, we know that his velocity is 50 mph due north. On the other hand, if Jordan just tells us that he drove 50 miles in 1 hour, we only know that his speed is 50 mph, and do not know his velocity since no direction was specified.

In the figure below, any of the rays (or vectors) shown indicate a specific velocity. The vectors all have the same magnitude (size), but they all point in different directions, so while they may all represent the same speed, they all have different velocities.

Another way to think of speed and velocity is to consider the movement of an object around a circle. To measure the average speed of an object that travels around a circle and returns to its starting point, divide the circumference of the circle (distance) by the amount of time it took the object to traverse the circle. If, for example, the circle has a circumference of 2π cm and the object travels around the circle in 2 seconds, the average speed of the object is:

In contrast, the average velocity of the object is 0. This is because average speed only considers the total distance traveled (2π cm) while average velocity is dependent on the change in position from start to end. Since the object returns to its starting position on the circle, the displacement of the object is 0, and therefore its velocity is 0.