Name: Date: Investigation 2.1 Speed and Velocity What is the difference between speed and velocity? People often use the terms speed and velocity interchangeably. While they are closely related, there is an important scientific difference between the two. Speed is a measure of the amount of distance traveled divided by the time taken to travel that distance. Velocity is the same measurement with the exception of the direction of travel being included. Velocity is speed with direction. In this investigation you will perform activities that will allow you to see the difference between speed and velocity. Finding the speed of the car Speed is the distance traveled by an object divided by the time taken to travel that distance. You have probably experienced talking about speed if you have ever discussed speed limits. Speed limits are the maximum speed a car may legally travel. These limits are given in miles per hour, which is the most common way to measure speed for cars. You can see that the words used imply a distance, given in miles, divided by a time, given in hours. This is the equation used to determine speed. If a speed limit of 60 miles per hour is listed on a sign, this indicates that the maximum speed a car can travel is 60 miles in 1 hour. A driver has a very handy tool for keeping track of his or her speed. It is called a speedometer, and it indicates the speed at which the car is traveling each moment the car is in operation. We are going to measure the speed of the car on the ramp. For measuring the speed of the car on the ramp we will use the units of centimeters per second. Speed = Distance traveled (cm) Time taken (s) We don t have a speedometer for our car, so you will measure the speed with one photogate and the DataCollector. With one photogate the DataCollector measures the time that the beam of the photogate is broken. As the car passes through the photogate, the light beam is broken for the width of the wing. The speed of the car is the width of the wing (the distance the car traveled), which is 1.00 cm divided by the time it takes to pass through the light beam (the time shown on the DataCollector as t A ). Setting up for speed 1. Make sure the ramp on the first hole of the physics stand. 2. Put at the 55 cm position. Record this position in Table 1. 3. Plug the photogate into the jack marked A on the back of the DataCollector. 4. Turn the DataCollector on and put it into CPO Timer mode. 5. Hold the car at the very top of the ramp and release the car without pushing it so it rolls on its own down the ramp. 6. Record the time through the photogate as it is displayed on the DataCollector for each trial. 7. Perform 5 trials. Release the car the same way for each trial. Investigation Answer Sheet: Speed and Velocity p.1
8. Calculate the speed of the car using the car wing length (1.00 cm) and the time measurement. Record this value in Table 1. Table 1: Car speed data Trial Position of (cm) (s) Distance traveled by car (cm) (1.00 cm) Speed of the car at 1 2 3 4 5 Analyzing your results a. What is the average of your five speed calculations for your car? b. Is that the speed of the car at every place on the ramp? c. How could you test your answer to question b? d. Come up with a quick way to test your answer. Set it up and try it out. Were you correct? Velocity You have found the speed of the car on the ramp. Now we will look at velocity. Figuring out velocity is not that different than figuring out speed. The one crucial difference is velocity is speed with direction. This means that one direction, like forward, is positive. The opposite direction, which would be backward, is considered negative. With this system in place, you can tell immediately the direction in which an object is moving. Investigation Answer Sheet: Speed and Velocity p.2
a. An object thrown straight up in the air is considered to have a positive velocity on its way up. How would its velocity change on the way down? b. How would the object s speed change on its way down? c. Can you think of a way to test to see if a car s speedometer really measures speed and not velocity? Calculating the velocity of the car on the ramp You will be performing a similar activity as the one you already completed when you found the speed of the car. For that activity you simply let the car roll all the way down the ramp and measured the speed of the car at the 55 cm position on the ramp. That told you the speed of the car at that particular position. For this next activity you will put the other photogate onto the ramp but it will not be used to measure a time interval. Instead, you will use a rubber band wrapped around the photogate to turn it into a rebounding device that will send the car back up the track. As the car passes through the photogate on the way down the ramp you will measure its time through. The car will then bounce off the rebounder, travel back up the ramp, and once again through the photogate. You will record both times and calculate the car s speed and its velocity. For this calculation we will consider moving down the ramp to be in the positive direction. a. If down the ramp is the positive direction, what would happen to the car s velocity if the car was moving back up the ramp? b. How would knowing the car s velocity let you know in which direction the car was moving? c. Can you think of another object or system that might need to use velocity instead of speed? Investigation Answer Sheet: Speed and Velocity p.3
Setting up for velocity 1. Make sure the ramp on the first hole of the physics stand. 2. Put at the 55 cm position again. 3. Place the other photogate onto the side of the ramp where the car rolls down as shown in the picture. 4. Secure the photogate in place directly across from the 70-cm mark. 5. Wrap a rubber band around the photogate to turn it into the rebounder. Make sure the rubber band is positioned in the center of the slot as shown in the picture. 6. Hold the car at the very top of the ramp and release the car without pushing it. 7. Once the car bounces off the rebounder and back through the photogate catch it so it doesn t roll back down the ramp again. 8. Construct a data table in your notebook similar to Table 2 below, for repeated trials. You will record two times through the photogate as it is displayed on the DataCollector for each trial. 9. To see the two times you need to hit the M button on the lower right of the DataCollector s screen. The M stands for memory, and this will allow you to measure the time through the photogate on the way down, and then back up. 10. The time displayed in the M column is the first time measured, so that is the time down the ramp. The time next to t A is the second measured time, so that will be the time back up the ramp. Record both times in their propper column in your table for each trial. 11. You will perform five trials. Release the car the same way every time for the top of the ramp to start each trial. 12. Calculate the velocity of the car moving down the ramp and also when moving back up the ramp using the car wing length (1.00 cm) and the time measurements. Record these value in your data table. Table 2: Car velocity data Trial down the ramp (s) back up the ramp (s) Velocity of the car down the ramp Velocity of the car back up the ramp 1 2 3 4 5 Investigation Answer Sheet: Speed and Velocity p.4
Thinking about what you observed a. What was the main difference between the velocity of the car moving down the ramp and the velocity of the car moving back up the ramp? b. What was the main difference between the speed of the car moving down the ramp and the speed of the car moving back up the ramp? c. What was the main difference between the velocity of the car moving back up the ramp and the speed of the car moving back up the ramp? d. What might another way to give the car a negative velocity? Investigation Answer Sheet: Speed and Velocity p.5