Speed describes how fast something is moving. A simple example would be to look at your car's speedometer while you are driving. This tells you the speed at which you are traveling. Notice that when you look your car's speedometer, it only tells you the speed at which you are traveling. It does not tell you the direction in which you are traveling. Of course, this seems obvious to anyone who drives a car, but I just wanted to make the point that speed does not involve a direction.

    How does speed describe motion? Well, this is also fairly obvious. For instance, when a car is moving at safe and legal speed of 55 mph (miles per hour), it will travel a distance of 55 miles in one hour of time. If it were moving at a speed of 100 mph, it would travel a distance of 100 miles in one hour of time. No surprises here.

    Next, let me define something called average speed. Average speed is defined a follows.

    Average Speed = [Distance Traveled]/[Time Taken to Travel that Distance]

    For instance, let's say that it takes you 2 hours to travel a distance of 100 miles. Using the above formula, your average speed during those 2 hours would be 50 miles/hour or 50 mph. This is because 100 miles divided by 2 hours is 50 miles/hour.

    Next, let's contrast average speed to instantaneous speed. Well, as you might have guessed, instantaneous speed is the speed at which you are currently traveling at the moment. For instance, if you are driving along and look down at the speedometer, your instantaneous speed at that moment would be what was displayed on your speedometer.

    So, how does instantaneous speed differ from average speed? Well, let's go back to the example above. One way to get an average speed of 50 mph over 2 hours would be to simply drive at 50 mph all the time. In this case, the average speed would be the same as the instantaneous speed. However, let's say your foot is not the steadiest part of your body. If this is true, then your instantaneous speed would fluctuate a lot. However, if you still manage to cover 100 miles in 2 hours, even though your speed was fluctuating, then your average speed would still be 50 mph, but your instantaneous speed during those two hours of driving would not always be 50 mph.

    Let me give a concrete example to illustrate this point. Let's say you drive at 25 mph for the first hour and then you drive at 75 mph for the second hour. In this case, your instantaneous speed during the first hour would be 25 mph at any moment. Your instantaneous speed during the second hour would be 75 mph at any moment. However, if you average those speeds (add them up and divide by two), you will find that the average speed was 50 mph. I hope this serves to illustrate the difference between instantaneous and average speed.

Velocity is very similar to speed except that it involves a direction as well as the speed. To determine the velocity of an object, you would need to know the object's speed and direction. To measure velocity in a car, you would need a speedometer and a compass. In essence, velocity gives you more information about an object.

Thought Question: Does constant speed necessarily imply constant velocity? Think about this before reading the next paragraph. In particular, think about the definitions of speed and velocity. Focus on the differences between the two definitions.

    The answer is no because the direction could be changing. Recall that velocity involves both speed and direction. Therefore, for a velocity to be constant, the speed and direction would both have to be constant. So, what would an object moving at a constant velocity look like? One answer would be that the object would not be moving at all. This is fine because the speed is 0 mph and the direction is not changing. The only other possible answer would be that the object is moving at a constant speed in a straight line. The constant speed part shouldn't be confusing. But, why does the object have to move in a straight line? Well, if it didn't move in a straight line, then the direction would be changing, and, as a result, the velocity would be changing and not constant.

    To summarize, the only way an object can have a constant velocity would be if it was sitting still or if it was moving in a straight line at a constant speed. There are no other alternatives.

Acceleration is defined as the change in velocity over time. This is also one of the concepts that people new to physics have a trouble grasping initially. Any time an object's velocity is changing, we say that the object is accelerating. This brings up an important point. In common language, when things speed up, we say that they are "accelerating", and, when they slow down, we say that they are "decelerating". However, in the language of physics, we say that both objects are accelerating, not because both objects are speeding up, but because both objects have changing velocities. This can be a confusing point at first. When I am using the word "accelerating" in terms of the common definition of the word, I will put it in quotes. For the physics definition, I will not use quotation marks.

    Finally, there is one more warning I'd like to offer about the definition of acceleration. Since acceleration involves a change in velocity, an object might be accelerating even though its speed is constant. Why is this possible? Well, it goes back to the difference between speed and velocity. Remember that velocity involves both speed and direction. So, a changing velocity does not have to necessarily involve a change in speed. It could just involve a change in direction.

    For example, consider a car moving at a constant speed of 55mph while turning in a circle. The car's velocity is not constant, even though the speed is constant. This is because the direction of motion is constantly changing while the car is turning. Since the direction is changing, even though the speed is not, the velocity is changing. (Remember, the velocity involves both speed and direction.) As a result, the car is accelerating, even though it is neither speeding up or slowing down. The car is accelerating because its velocity is changing.