Instantaneous Velocity: Definition & Formula

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  • 0:00 Definition of…
  • 1:51 Difference Between…
  • 3:05 A Better Definition
  • 3:50 Instantaneous Velocity Formula
  • 5:56 Lesson Summary
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Lesson Transcript
Instructor: Josh Corbat

Josh has taught Earth Science and Physical Science at the High School level and holds a Master of Education degree from UNC-Chapel Hill.

When driving, never take your eyes off the road! That said, it's necessary to occasionally glance at the speedometer. When you do, you are reading your instantaneous velocity. This lesson explores the science behind instantaneous velocity.

Definition of Instantaneous Velocity

You worked hard all week and it's finally here: the weekend. You and some friends decide to take a short trip to your favorite spot just a few hours' drive from where you live (for me, it's the beach). You're cruising along the freeway, listening to music without a care in the world. But you start to care when you see a parked police vehicle on the side of the road. You start to care a lot. You frantically glance at your speedometer and see that you are a few miles under the limit. You continue to cruise, recovering from your momentary panic.

The reading you took from the car's speedometer is instantaneous, meaning it represents only a single moment in time. If you were to watch the speedometer, take notes on the readings, and average them, you would have an average reading. For our purposes in this lesson, we'll focus on instantaneous measurements.

To most people, the word velocity means how fast something is traveling. Those people are not wrong. Velocity does, indeed, refer to the quickness or slowness of something, and by that simplified definition, instantaneous velocity is the velocity reading (how fast or slow you're going) at a particular point in time.

This may be the common definition of velocity applied in everyday speech, but scientists would disagree slightly. They would say that this simplified definition is actually the definition of speed, and that there is actually slight scientific difference between velocity and speed. Let's explore this further.

The Difference Between Velocity and Speed

Let's start with speed. Speed is defined as the rate of distance of travel over time. Simply put, this means that speed is the distance you travel divided by the time it took to travel that distance. So, it is how fast or slow you are moving. Speed is all about this change in distance over an amount of time; it has nothing to do with the direction you're traveling.

Velocity, on the other hand, takes into account the direction an object is traveling. It still is concerned with the speed, but the direction must also be reported. An example of a speed is '45 miles per hour.' An example of velocity is '45 miles per hour west.' In the real world, people often ignore the importance of including direction in a velocity measurement, so the words speed and velocity sometimes become interchangeable. If you tell someone your instantaneous velocity when unfortunately passing a parked police vehicle was 90 miles per hour, they probably wouldn't prompt you for the direction.

A Better Definition

Using what we now know about the difference between velocity and speed, we can better define instantaneous velocity as the rate of change in the position of an object over time. Let's focus on the part of that definition that says, 'the position of an object.' It's easiest to think about position as if you're referring to a map or coordinate plane. On both of these reference systems, a change in position measures both distance and direction. Since velocity includes the direction traveled, this definition is much more complete and accurate than the one many people use interchangeably with the definition of speed.

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