12A How do scientists describe motion? The average speed is the ratio of the distance traveled divided by the time taken. This is an idea you already use. For example, if your car is moving at a speed of 60 miles per hour that means the ratio of the distance the car moves divided by the time it takes is always equal to 60 miles/hour. If you go 120 miles in 2 hours, your average speed is 60 miles per hour because the ratio 120 miles/2 hours equals 60 miles/hour. Materials Energy car and track Timer and photogates Rubber band A The relationship between distance, time, and speed In science, you will mostly be working with speeds in units of centimeters per second (cm/s) or meters per second (m/s). a. A duck swims 10 meters in 5 seconds. What is the average speed of the duck? b. A car on cruise control is moving at a constant speed of 55 mph. How far does the car travel in three hours? c. A jet aircraft is moving at a constant speed of 500 kilometers per hour. How long does it take the jet to travel 2,000 kilometers? 1
B Setting up for constant speed 1. Put the track together as shown in the diagram. Use one rubber band on the launching end and a ball of clay on the catching end to stop the car. 2. Adjust the stop so the rubber band has 2-3 cm of deflection. Put a photogate on the mark just ahead of the car. Practice launching the car until you can get 3 successive photogate times to within 0.0010 seconds of each other. C Making the car move at constant speed 1. Put two photogates on the track. 2. Adjust the height of the feet on one end or the other until the times from photogates A and B are within 0.0010 seconds of each other. You may also use a thin book or pad of paper to prop up one end. 3. Be careful not to disturb the track once you get it set up. 2
D Stop and think a. Describe how the photogate measurements prove that the car has constant speed, or nearly constant speed. b. Calculate the speed of the car in meters per second (m/sec). E Measuring position versus time 1. Put photogate A near the start so the car breaks the light beam just after it is launched. 2. Move photogate B to different positions 10 cm apart along the track (measure position). 3. For every position of photogate B, record the time through the beam at photogates A and B and also the time from A to B. 4. Take at least 6 data points along the track being careful to start the car the same way every time. Use photogate A to test whether you should keep the data from a trial or do it over. Position (cm) Table 1: Position versus time data Time through photogate A Time through photogate B Time from photogate A to B 3
F Making the position versus time graph a. Start the graph by putting the position of the car on the vertical (y) axis. Position is where you placed photogate B. b. Put the time from photogate A to B on the horizontal (x) axis. This is the time that the car has traveled between A and B. c. Finish the graph by plotting the points from Table 1 and giving the graph a title. G Stop and think a. What shape does the position versus time graph have? Describe the line or curve that you get. b. Calculate the average speed of the car from the graph or your data. c. How long would it take the car to travel a distance of 2 meters if it kept the same speed? 4
d. The car moved at a constant speed as it rolled along the level track. What would happen to the speed of the car as it rolled down a track placed at a steep angle? e. What shape would the graph have if the car was speeding up as it went down the track? f. What shape would the graph have if the car was moving at a constant speed that was double the average speed of your car? g. How is the shape of the position versus time graph related to the speed of the car? 5