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Is it possible to drive with a speed of 100 mph but a velocity of 0? In this lesson, we will examine the difference between speed and velocity and use that information to answer this question.

Physics at the Race Track

Every year in late February, race fans flock to Daytona, Florida, for a 500-mile auto race. The Daytona 500 has become an American institution, watched by millions of people throughout the world. In 2013, Jimmie Johnson took the checkered flag, winning the race with a blistering average speed of 159 miles per hour! Physics pop quiz time: What was Jimmie Johnson's average velocity? Be honest, how many of you said 159 miles per hour? The correct answer is 0 miles per hour. The reason for this dramatic difference lies in the subtle distinction between speed and velocity.

Speed

The best way to start examining the difference between speed and velocity is to look at your car's speedometer. The next time you're in your car on the highway, do just that. What does it say? I'm going to assume you always obey the speed limit, so if the speed limit is 65 miles per hour, your speedometer should read 65 miles per hour. This means that if you drive for 65 miles, it will take you an hour.

It doesn't matter where you're driving to, how many turns the road takes, or if you're on a big, circular track. Speed is only concerned with how much ground you've covered in the time you've been driving. To put an official definition on it, speed is how much distance is covered over a specific period of time, regardless of direction traveled. Since there is no directional component, speed must be a scalar quantity.

In physics, you can calculate average speed by taking the total distance traveled and dividing it by the total time required to travel that distance.

Average speed = total distance / time

So, if we know Jimmie Johnson drove 500 miles, and I tell you it took 3.14 hours, we can calculate his average speed.

Average speed = 500 miles / 3.14 hours = 159 miles/hour

Remember, for the speed, it doesn't matter that he was driving in a big circle. But that circle will matter soon.

Velocity

Speed is a scalar quantity, so you can probably guess that speed has a corresponding vector quantity that combines how fast an object is traveling and its direction of travel. This vector quantity is velocity, defined as the rate at which an object changes position.

Remember that in physics a change in position from its starting point to its end point is an object's displacement. The exact route doesn't matter here - only the direct distance from start to finish. Displacement always has both a magnitude and a direction.

Let's look at the equation for average velocity:

Average velocity = displacement / time

In this equation, velocity is represented by a letter v with a bar over it. This line indicates we want an average. The change in displacement is delta s, and the change in time is delta t.

To illustrate velocity, let's go back to Daytona. We calculated Jimmie Johnson's average speed, but what about his average velocity? Daytona speedway is shaped as seen below. The point on the track where the car is serves as both the starting line and the finish line.

If we trace Jimmie's path along the track for one lap, he starts and ends at the same position, making his total displacement 0. Even though he drives many laps and covers 500 miles, he always starts and ends at the same point, making his total displacement for the entire race 0. To calculate his average velocity:

Average velocity = 0 miles / 3.14 hours = 0 miles/hour

As you can see, his speed was 159 miles per hour, but his velocity was 0 miles per hour.

Examples of Average Velocity

But solving for velocity and getting 0 probably doesn't help very many people understand this. Let's look at another velocity problem to try and make things clearer. You decide to walk from your house to the store, taking the blue route below to get there. You cover 225 meters total. The walk takes you 2 hours.

First, let's find your average speed.

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Average speed = total distance / time = 225m / 2 hr = 113 m/hr

Now, let's solve for the average velocity. Remember, velocity depends on total displacement, not total distance traveled. In this case, you walked a distance of 225 meters in 2 hours, but your displacement from your starting position (your house) to your final position (the store) is only 54.1 meters northeast, represented by the green line.

Average velocity = displacement / time

Displacement = Delta s = 54.1 m NE

Average velocity = 54.1 m northeast / 2hr = 27.1 m/hr NE

Since velocity is a vector quantity, you must remember to include which direction you moved. In this case, the store is north and east of your house, so you moved at an average velocity of 27.1 meters every hour in a northeasterly direction. The velocity does not care that you walked east first, then south, then east again, and so on, only that you ended up northeast of where you started.

Velocity Trick Questions?

I want to end this lesson with a couple of questions to test your understanding of these two concepts.

Number 1: Can you move with a constant speed but not a constant velocity?

Pause for a minute if you want to think about this question. Ready for the answer? The answer is yes. Walk in a circle, making sure you walk the same speed the entire time. Since you're constantly changing direction, your velocity is changing even though your speed is not. A constant velocity requires both a constant speed and an unchanging direction.

Number 2: Can you move with a constant velocity but not a constant speed?

Take a minute. Ready? The answer here is no. Like I just stated, constant velocity requires both a constant speed and an unchanging direction. If you change your speed at all, even if you are moving in a straight line, your velocity must change.

Lesson Summary

Let's review.

Speed and velocity are related concepts in physics. Speed is how much distance is covered over a specific period of time, regardless of direction traveled. Speed is a scalar quantity and can be calculated by the following equation:

Average speed = total distance / time

Velocity is the rate at which an object changes position. When calculating velocity, you must take into account the total displacement of the object, not the total distance traveled by that object. Both displacement and velocity are vector quantities, so you must include a direction of travel to be correct. The equation for velocity is:

Average velocity = displacement / time

Learning Outcomes

Upon completing this lesson, you will be able to:

Define speed and velocity

Recall the formulas for finding velocity and speed

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