Introducing Speed
How fast or slow something moves is its speed. Speed determines how far something travels in a given amount of time. The SI unit for speed is meters per second (m/s). Speed may be constant, but often it varies from moment to moment. Average Speed Even if speed varies during the course of a trip, it’s easy to calculate the average speed by using this formula: For example, assume you go on a car trip with your family. The total distance you travel is 120 miles, and it takes 3 hours to travel that far. The average speed for the trip is: Q: Terri rode her bike very slowly to the top of a big hill. Then she coasted back down the hill at a much faster speed. The distance from the bottom to the top of the hill is 3 kilometers. It took Terri ¼ hour to make the round trip. What was her average speed for the entire trip? (Hint: The roundtrip distance is 6 km.) A: Terri’s speed can be calculated as follows: Instantaneous SpeedWhen you travel by car, you usually don’t move at a constant speed. Instead you go faster or slower depending on speed limits, traffic lights, the number of vehicles on the road, and other factors. For example, you might travel 65 miles per hour on a highway but only 20 miles per hour on a city street. You might come to a complete stop at traffic lights, slow down as you turn corners, and speed up to pass other cars. Therefore, your speed at any given instant, or your instantaneous speed, may be very different than your speed at other times. Instantaneous speed is much more difficult to calculate than average speed. If you want to learn more about calculating speed, watch the video at this URL. This text was adapted from CK12.com. It is licensed under the Creative Commons (CC BYNC 3.0) Speed and Direction Speed tells you only how fast or slow an object is moving. It doesn’t tell you the direction the object is moving. The measure of both speed and direction is called velocity. Velocity is a vector. A vector is measurement that includes both size and direction. Vectors are often represented by arrows. When using an arrow to represent velocity, the length of the arrow stands for speed, and the way the arrow points indicates the direction. If you’re still not sure of the difference between speed and velocity, watch the cartoon at this URL. The arrows in the Figure represent the velocity of three different objects. Arrows A and B are the same length but point in different directions. They represent objects moving at the same speed but in different directions. Arrow C is shorter than arrow A or B but points in the same direction as arrow A. It represents an object moving at a slower speed than A or B but in the same direction as A. 

Calculating Average Velocity
You can calculate the average velocity of a moving object that is not changing direction by dividing the distance the object travels by the time it takes to travel that distance. You would use this formula: This is the same formula that is used for calculating average speed. It represents velocity only if the answer also includes the direction that the object is traveling. Let’s work through a sample problem. Toni’s dog is racing down the sidewalk toward the east. The dog travels 36 meters in 18 seconds before it stops running. The velocity of the dog is: Note that the answer is given in the SI unit for velocity, which is m/s, and it includes the direction that the dog is traveling. Q: What would the dog’s velocity be if it ran the same distance in the opposite direction but covered the distance in 24 seconds? A: In this case, the velocity would be. This text was adapted from CK12.com. It is licensed under the Creative Commons (CC BYNC 3.0) Defining Acceleration Acceleration is a measure of the change in velocity of a moving object. It measures the rate at which velocity changes. Velocity, in turn, is a measure of the speed and direction of motion, so a change in velocity may reflect a change in speed, a change in direction, or both. Both velocity and acceleration are vectors. A vector is any measurement that has both size and direction. People commonly think of acceleration as in increase in speed, but a decrease in speed is also acceleration. In this case, acceleration is negative and called deceleration. A change in direction without a change in speed is acceleration as well. Q: Can you think of an example of acceleration that doesn’t involve a change in speed? A: Driving at a constant speed around a bend in a road is one example. Use your imagination to think of others. When describing velocity should describe how both direction and speed are changing. For example, a boy on the carousel is moving up and down and around in a circle, so his direction is constantly changing, but his speed changes only at the beginning and end of the ride. A skydiver is falling straight down toward the ground so her direction isn’t changing, but her speed keeps increasing as she falls until she opens her parachute. 