8.1 The Language of Motion Vectors vs. Scalars. Distance vs. Displacement. Example. Two main types of quantities:


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1 8.1 The Language of Motion Vectors vs. Scalars Two main types of quantities: Scalars: Describe magnitude but not direction. (Magnitude is the size of a measurement) Example: Johnny walked 25 km Vectors: Describe magnitude and direction. Example: Johnny walked 25 km North Every time you use a map or give directions, you are using vectors. You can always tell if a quantity is a vector because there will be an arrow drawn above it. Example: A scalar has no arrow. Example: Distance vs. Displacement Distance (d) is a scalar that tells you how far something has travelled. Example: Johnny ran a distance of 400 m Displacement (d) is a vector that describes your position relative to where you started. Example: Johnny ran 400 m North of his home. Example A car leaves home and drives 10 km to the store and then returns home. The car has driven a total distance of 20 km but its final displacement is 0 km. We measure both distance and displacement in metres (m). 1
2 Time Interval Time interval or change in time is calculated by: Example Where: t = change in time (the symbol is the greek letter delta. It means change. t i = initial time t f = final time The time interval to move from the fire hydrant to the sign is calculated by: Displacement Displacement or change in position is calculated by: Displacement and Distance Where: = change in position or displacement = initial position = final position Between 2 s and 5 s, the skateboarder s: displacement is 5 m [E] and distance travelled is 5 m. 2
3 Watch for Signs Turn to page 349 for common sign conventions Copy Figure 8.8 into notes Uniform Motion Uniform motion is a term that describes objects that do not speed up, slow down, or change direction. Turn to page 352 in textbook and do Activity 81B In other words, they travel at constant velocities (we will discuss velocity more later) Example The position of the ball in this photo is shown at equal time intervals. How would you determine if this motion is uniform motion? What would the picture look like if the ball was NOT in uniform motion? Graphing Uniform Motion Motion of an object can be analyzed by drawing a positiontime graph. A positiontime graph plots position data on the vertical axis (yaxis) and time data on the horizontal axis (xaxis). 3
4 Positive Slope Uniform motion is represented by a straight line on a positiontime graph. Slants up to the right. Indicates an object travelling in the positive direction (ie: North, East, to the right, up, etc.) Horizontal line. Indicates that the object is stationary. Zero Slope Slants down to the right. Indicates an object travelling in the negative direction (ie: South, West, to the left, down, etc.) Negative Slope 4
5 Ch. 8.2 Average Velocity Speed ( ) is the distance an object travels divided by the time to travel that distance. In other words Speed is a scalar quantity (no direction). These two ski gondolas have the same speed but have different velocities since they are travelling in opposite directions. Velocity ( ) is the displacement of an object divided by the time interval. In other words Velocity describes how fast an object s position is changing. Velocity is a vector quantity (direction). The units for velocity and speed are metres per second (m/s). Calculating the Slope of the PositionTime Graph To learn more about velocity, we must now understand straight line graphs. The slope of a graph is represented by rise = change in yaxis run = change in xaxis Finding the Slope of a Line 1. Pick two points on the grid. 2. Make a triangle Units = metres/second So slope = Position (m) Time(s) 5
6 Position Time Graph Example On a positiontime graph the slope is the change in position ( ) divided by the change in time ( ). Which jogger s motion has a greater slope? Which jogger is moving faster? What is the slope of each line? What is each jogger s? Average Velocity Usually, objects do not move at a perfectly constant speed. For this reason, we often use average velocity in our calculations. The slope of a positiontime graph is the object s average velocity ( ). Average velocity is the rate of change in position for a time interval. Remember, (average velocity), is a vector and we must therefore always include a direction. If we were to discuss, (average speed), we do not need to include direction, because speed is a scalar. 6
7 On a positiontime graph if forward is given a positive direction: A positive slope = the object s average velocity is forward. A negative slope = the object s average velocity is backwards. Calculating Average Velocity The relationship between average velocity, displacement, and time is given by: Example 1 1. What is the average velocity of a dog that takes 4.0 s to run forward 14 m? Zero slope = the object s average velocity is zero (not moving). Example 2 A boat travels 280 m East in a time of 120 s. What is the boat s average velocity? Calculating Displacement The formula for finding velocity can be rearranged so that you can solve for either displacement or time. You can solve for displacement by taking this equation and multiplying both sides by t leaving the equation: 7
8 Example 3 What is the displacement of a bicycle that travels 8.0 m/s [N] for 15 s? Example 4 Solve this problem on your own, using the same steps. A person, originally at the starting line, runs west at 6.5 m/s. What is the runner s displacement after 12 s? Calculating Time Use the last equation to solve the following: 1. How long would it take a cat walking north at 0.80 m/s to travel 12 m north? Solution: 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 For example, convert 75 km/h to m/s. 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? 8
9 Converting between m/s and km/h Another Example: 1. Convert 95 km/h to m/s. Try the following unit conversion problems yourself. 2. A truck s displacement is 45 km north after driving for 1.3 hours. What was the truck s average velocity in km/h & m/s? 3. What is the displacement of an airplane flying 480 km/h [E] during a 5.0 min time interval? 9
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