In order to determine speed you must know

• Daniel Codoluto

  Daniel was a teaching assistant for college level physics at the University of Texas at Dallas and the University of Denver for a combined two years. He earned a Master of Science in Physics at the University of Texas at Dallas and a Bachelor of Science with a Major in Physics and a Minor in Astrophysics at the University of Minnesota.

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• Instructor John Simmons

  John has taught college science courses face-to-face and online since 1994 and has a doctorate in physiology.

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Study the speed and velocity definitions and compare speed vs. velocity to note the difference. Understand how to calculate velocity and speed using the formulas. Updated: 04/23/2022

Two important quantities that play a role in describing the motion of an object are speed and velocity. Both quantities provide information about an object's trajectory, but speed is classified as a scalar quantity, while velocity is known as a vector quantity. A scalar quantity contains information about magnitude. A vector quantity, on the other hand, contains information about magnitude along with direction. An object's speed is useful for describing how fast an object moves, while velocity involves an object's displacement in relation to some point. Displacement is a means to locate an object in relation to some reference point. It is a change in position from one point to another.

Speed and velocity may describe how fast an object moves, but use different notions for locating an object. For example, a car driving on a highway moves at 60 miles per hour. This is the vehicle's speed shown on a speedometer. It is simply tracking how much distance is being covered during some time period, without any reference to the vehicle's relative location. However, if the car has moved 60 miles on the highway in one hour going west, then the vehicle's velocity is 60 miles per hour west. In this case, the direction of the vehicle is known. The magnitude of the velocity and the speed of an object can differ because they involve different means of locating an object, namely, displacement and distance.

Speed and Velocity: Concepts

Did you know that speed and velocity are different? Most people consider speed and velocity to be the same and may even use these terms interchangeably. While speed and velocity are similar, they are definitely not the same. So, how are they different? Speed is a matter of how fast an object is moving regardless of the direction it's going, whereas velocity is a matter of how fast an object gets somewhere with respect to direction. Think of a person repeatedly taking two steps forward and then two steps back. They are moving, but they're not getting anywhere. In other words, they have speed, but no velocity. In short, speed is a measure of how fast an object moves, while velocity is a measure of how fast an object gets somewhere.

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What is Speed?

Speed is defined as the magnitude of the velocity of an object and is often expressed in units of meters per second (m/s), but the units of speed are always in units of length/time. It is measured by the total distance covered by an object per unit time.

For instance, if a person starts at point A, walks 5 meters to point B, and then walks another 5 meters to point C, then the total distance traversed is 10 meters, independent of direction. If the person traveled this distance in 100 seconds, then the speed, however, is 0.1 m/s. Since only the magnitude of the value is known and information about direction is not, speed is considered a scalar quantity.

What is Velocity?

Velocity is defined as the displacement traversed by an object per unit time and can also be expressed in meters per second (m/s). Other forms of units of length/time may be used to express velocity as well. It is the ratio of displacement that occurs during some known time interval to that same time interval, or the rate of change in displacement with respect to time. Displacement is the difference in position from one point to another point. It is considered a vector quantity, since it contains information regarding direction.

To see how displacement differs from distance, consider a person that starts at point A, walks 5 meters to point B, and then walks back to point A. The total displacement is zero meters, whereas the distance covered is 10 meters. If an object moves from point to point, then the displacement is the vector sum of the paths taken. The vector sum is itself a vector, therefore, displacement is a vector quantity.

How to Calculate Speed and Velocity

Speed is calculated by taking the ratio of distance traveled by an object during a time interval to that interval. Velocity, on the other hand, is found by taking the ratio of a displacement interval during a time to that time taken. The result for speed will just be a number, or a scalar, whereas the result for velocity will be a number that includes information about direction, or a vector.

Velocity Formula

Velocity is calculated by finding the ratio of the displacement of an object during a time period to that time period. It is expressed by the velocity formula:

{eq}\text{velocity} = \frac{\text{displacement} }{\text{time} } {/eq}.

Definitions of Velocity and Speed

Before we discuss the formulas for calculating speed and velocity, we need to consider more detailed definitions of each term. Speed is defined as the rate of change in distance with respect to time. Velocity is defined as the rate of change in displacement with respect to time. Notice the words distance and displacement are the only difference between the two definitions.

So, what's the difference between distance and displacement? Distance refers to the total amount of ground covered by an object in motion, whereas displacement refers to the net change in position of an object in motion. Distance is what we call a scalar quantity because distance is fully described by magnitude alone with no reference to direction. Since speed is a function of distance, speed is a scalar quantity as well. Displacement is a vector quantity because displacement is fully described with both magnitude and direction. Since velocity is a function of displacement, velocity is a vector quantity. If we combine the definitions of speed and velocity, one could say that velocity is speed with direction and that would be accurate.

Formula for Speed

Now that we understand the concepts of speed and velocity, we can examine the formulas for calculating these measures. Let's take a look at speed first. As discussed, speed is the rate of change in distance in a period of time. In other words, speed is a function of both distance and time. As such, the formula for calculating speed includes both distance and time, where speed is directly proportional to the change in distance and inversely proportional to the change in time.

Let's take a look at the formula for speed: Speed = distance ÷ time

Let's use an example to practice calculating speed. Consider a man walking in a zigzag pattern. If the man covers a total of 20 meters in the zigzag, then the change in distance is equal to 20 meters. Now, let's say he takes 60 seconds to cover that 20-meter zigzag pattern. Therefore, the change in time is 60 seconds. We can put these values together in our formula and calculate for speed.

Let's first recall the formula for speed: Speed = distance ÷ time

Now, plug in the observed values: Speed = 20 meters ÷ 60 seconds

20 divided by 60 equals 0.33. Therefore, the man is moving with a speed of 0.33 meters per second. This can be expressed as Speed = 0.33 m/sec, where m = meters and sec = seconds. You may be more familiar with speed expressed as miles per hour, or simply MPH.

Speed and Velocity: Concepts

Did you know that speed and velocity are different? Most people consider speed and velocity to be the same and may even use these terms interchangeably. While speed and velocity are similar, they are definitely not the same. So, how are they different? Speed is a matter of how fast an object is moving regardless of the direction it's going, whereas velocity is a matter of how fast an object gets somewhere with respect to direction. Think of a person repeatedly taking two steps forward and then two steps back. They are moving, but they're not getting anywhere. In other words, they have speed, but no velocity. In short, speed is a measure of how fast an object moves, while velocity is a measure of how fast an object gets somewhere.

Definitions of Velocity and Speed

Before we discuss the formulas for calculating speed and velocity, we need to consider more detailed definitions of each term. Speed is defined as the rate of change in distance with respect to time. Velocity is defined as the rate of change in displacement with respect to time. Notice the words distance and displacement are the only difference between the two definitions.

So, what's the difference between distance and displacement? Distance refers to the total amount of ground covered by an object in motion, whereas displacement refers to the net change in position of an object in motion. Distance is what we call a scalar quantity because distance is fully described by magnitude alone with no reference to direction. Since speed is a function of distance, speed is a scalar quantity as well. Displacement is a vector quantity because displacement is fully described with both magnitude and direction. Since velocity is a function of displacement, velocity is a vector quantity. If we combine the definitions of speed and velocity, one could say that velocity is speed with direction and that would be accurate.

Formula for Speed

Now that we understand the concepts of speed and velocity, we can examine the formulas for calculating these measures. Let's take a look at speed first. As discussed, speed is the rate of change in distance in a period of time. In other words, speed is a function of both distance and time. As such, the formula for calculating speed includes both distance and time, where speed is directly proportional to the change in distance and inversely proportional to the change in time.

Let's take a look at the formula for speed: Speed = distance ÷ time

Let's use an example to practice calculating speed. Consider a man walking in a zigzag pattern. If the man covers a total of 20 meters in the zigzag, then the change in distance is equal to 20 meters. Now, let's say he takes 60 seconds to cover that 20-meter zigzag pattern. Therefore, the change in time is 60 seconds. We can put these values together in our formula and calculate for speed.

Let's first recall the formula for speed: Speed = distance ÷ time

Now, plug in the observed values: Speed = 20 meters ÷ 60 seconds

20 divided by 60 equals 0.33. Therefore, the man is moving with a speed of 0.33 meters per second. This can be expressed as Speed = 0.33 m/sec, where m = meters and sec = seconds. You may be more familiar with speed expressed as miles per hour, or simply MPH.

What is velocity in science?

Velocity in science is a concept that describes how fast an object or particle moves relative to some reference point. It involves the displacement of an object and also possesses information about the direction of motion of an object at a given instant.

What is velocity in a simple definition?

Velocity is defined as the rate of change in displacement of an object or particle with respect to time. In other words, it is the ratio of displacement that occurs during a known time interval to that same time interval. It contains information about both magnitude and direction, so it is a vector quantity.

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