## 3.4 Speed and Velocity

What is the difference between speed and velocity? Basically, velocity is speed in a given direction. A car has a speedometer not a velocitometer because it only tells the driver how fast he is going. If it also gave the direction the driver was going, it could be a velocitometer. In physics, velocity is more important than speed because it tells you more about the object’s motion. Always, the more you know, the better.

Again, speed has no direction, velocity does. Speed is the magnitude of the velocity. In this class we will use the two terms almost interchangeably. This is because you are learning about linear motion right now. There are only two directions with linear motion- that way and the opposite of that way. It will get more complicated when we discuss planar motion. Objects not only go forward/backward, but also up/ down or right/left.

You can’t go a negative speed, but you can go a negative velocity. From your math class you learned that negative means opposite. So a car that is going at a velocity of 25 m/s is moving differently than a car with a velocity of -25 m/s. If the first car is going East, then the other car is traveling the opposite of East, West.

Again, speed has no direction, velocity does. Speed is the magnitude of the velocity. In this class we will use the two terms almost interchangeably. This is because you are learning about linear motion right now. There are only two directions with linear motion- that way and the opposite of that way. It will get more complicated when we discuss planar motion. Objects not only go forward/backward, but also up/ down or right/left.

You can’t go a negative speed, but you can go a negative velocity. From your math class you learned that negative means opposite. So a car that is going at a velocity of 25 m/s is moving differently than a car with a velocity of -25 m/s. If the first car is going East, then the other car is traveling the opposite of East, West.

## Click __HERE __for more practice with Speed and Velocity

## 3.4 Sample Problem

**100 Meter Dash**

One of the fastest men in world history is Maurice Greene of the USA. Maurice Greene ran 100 meters in 9.79 seconds in 1999. This gave him an average speed of 10.21 m/s (22.84 mi/hr). Was this his instantaneous speed throughout the course of the race?

At the beginning of the race, a sprinter in the starting blocks has a speed of zero. When the gun goes off, the objective is to accelerate quickly away from the starting blocks and reach maximum speed as soon as possible, and hold that speed for the remainder of the race. A typical runner does not reach top speed until he has traveled 15 to 20 meters. By comparison, the cheetah reaches its top speed after only two or three steps.

If the typical world-class sprinter has an average speed of approximately 10 m/s over the course of 100 m, the maximum speed must be higher than this value. This is because the instantaneous speed is less than the average speed while the sprinter is accelerating. The graph of Maurice Greene’s record run might look something like this (red line):

To determine his average speed for the entire race all you need are his initial position and time and his final position and time. His average speed is (100 m - 0 m)/(9.79s - 0s) = 10.21 m/s.

Looking closely at the graph, you will see that the slope of the curve is shallow at the beginning and much steeper at the end of his sprint. This means that although his average speed was 10.21 m/s, he had to have been going slower than that at the beginning, and faster than that at the end of the race.

To get his instantaneous speed just pick two points on the graph that are close together. The closer the times are to each other, the closer to an instant of time that you have.

Maurice Greene’s speed from 0 to 2 s is 2.5 m/s while from 2 to 4 s it is 5.0 m/s. From 6 to 8 s, his speed is 15.0 m/s. The slope of the line on the (red) graph gets steeper and steeper the faster he goes.

Looking closely at the graph, you will see that the slope of the curve is shallow at the beginning and much steeper at the end of his sprint. This means that although his average speed was 10.21 m/s, he had to have been going slower than that at the beginning, and faster than that at the end of the race.

To get his instantaneous speed just pick two points on the graph that are close together. The closer the times are to each other, the closer to an instant of time that you have.

Maurice Greene’s speed from 0 to 2 s is 2.5 m/s while from 2 to 4 s it is 5.0 m/s. From 6 to 8 s, his speed is 15.0 m/s. The slope of the line on the (red) graph gets steeper and steeper the faster he goes.