Speed ( v ) is the distance an object travels during a given time interval divided by the time interval.
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1 v 8.2 Average Velocity Speed ( v ) is the distance an object travels during a given time interval divided by the time interval. Speed is a scalar quantity. The SI unit for speed is metres per second (m/s). Velocity ( v ) is the displacement of an object during a time interval divided by the time interval. Velocity describes how fast an object s position is changing. Velocity is a vector quantity and must include direction. The direction of the velocity is the same as the direction of the displacement. The SI unit for velocity is metres per second (m/s). These two ski gondolas have the same speed but have different velocities since they are travelling in opposite directions. See pages
2 Calculating the Slope of the Position-Time Graph The slope of a graph is represented by rise/run. This slope represents the change in the y-axis divided by the change in the x-axis. On a position-time graph the slope is the change in position ( d ) divided by the change in time ( t). The steeper the slope the greater the change in displacement during the same time interval. slope d t Which jogger s motion has a greater slope? Which jogger is moving faster? See pages
3 Average Velocity The slope of a position-time graph is the object s average velocity. Average velocity is the rate of change in position for a time interval. The symbol of average velocity is: v av On a position-time graph, if forward is given a positive direction: A positive slope means that the object s average velocity is forward. A negative slope means that the object s average velocity is backward. See pages Zero slope means the object s average velocity is zero.
4 Calculating Average Velocity The relationship between average velocity, displacement, and time is given by: Use the above equation to answer the following questions. 1. What is the average velocity of a dog that takes 4.0 s to run forward 14 m? v av d t 2. A boat travels 280 m east in a time of 120 s. What is the boat s average velocity? Answers are on the next slide. See page 368
5 Calculating Average Velocity The relationship between average velocity, displacement, and time is given by: Use the above equation to answer the following questions. 1. What is the average velocity of a dog that takes 4.0 s to run forward 14 m? (3.5 m/s forward) v av d t 2. A boat travels 280 m east in a time of 120 s. What is the boat s average velocity? (2.3 m/s east) See page 368
6 Calculating Displacement The relationship between displacement, average velocity, and time is given by: Use the above equation to answer the following questions. 1. What is the displacement of a bicycle that travels 8.0 m/s [N] for 15 s? d v av t 2. A person, originally at the starting line, runs west at 6.5 m/s. What is the runner s displacement after 12 s? Answers are on the next slide.
7 Calculating Displacement The relationship between displacement, average velocity, and time is given by: Use the above equation to answer the following questions. 1. What is the displacement of a bicycle that travels 8.0 m/s [N] for 15 s? (120 m [N]) d v av t 2. A person, originally at the starting line, runs west at 6.5 m/s. What is the runner s displacement after 12 s? (78 m west)
8 Calculating Time The relationship between time, average velocity, and displacement is given by: Use the above equation to answer the following questions. 1. How long would it take a cat walking north at 0.80 m/s to travel 12 m north? t d v av 2. A car is driving forward at 15 m/s. How long would it take this car to pass through an intersection that is 11 m long? Answers are on the next slide.
9 Calculating Time The relationship between time, average velocity, and displacement is given by: Use the above equation to answer the following questions. 1. How long would it take a cat walking north at 0.80 m/s to travel 12 m north? (15 s) t d v av 2. A car is driving forward at 15 m/s. How long would it take this car to pass through an intersection that is 11 m long? (0.73 s)
10 Converting between m/s and km/h To convert from km/h to m/s: Change km to m: 1 km = 1000 m Change h to s: 1 h = 3600 s Multiply by 1000 and divide by 3600 or Divide the speed in km/h by 3.6 to obtain the speed in m/s. For example, convert 75 km/h to m/s. 75 km 1h 1000m 1h 21m/s 1km 3600s Speed zone limits are stated in kilometres per hour (km/h).
11 Converting between m/s and km/h Try the following unit conversion problems. 1. Convert 95 km/h to m/s. 2. A truck s displacement is 45 km north after driving for 1.3 h. What was the truck s average velocity in km/h and m/s? 3. What is the displacement of an airplane flying 480 km/h [E] during a 5.0 min time interval? Answers are on the next slide.
12 Converting between m/s and km/h Try the following unit conversion problems. 1. Convert 95 km/h to m/s. (26 m/s) 2. A truck s displacement is 45 km north after driving for 1.3 h. What was the truck s average velocity in km/h and m/s? (35 km/h [N], 9.6 m/s [N]) 3. What is the displacement of an airplane flying 480 km/h [E] during a 5.0 min time interval? (40 km [E] or 40, 000 m [E]) Take the Section 8.2 Quiz
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