Motion: 8.2 THURSDAY APRIL 17 th Cheetah clip (c) McGraw Hill Ryerson 2007

8.2 Average Velocity You will learn the difference between speed and velocity and how to use position-time graphs to calculate average velocity. (c) McGraw Hill Ryerson 2007

Questions What is speed? What is velocity? What is the difference between them? (c) McGraw Hill Ryerson 2007

The need for speed. Speed ( ) 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). See pages

Remember this slide from 8.1 Scalar Distance - d  SI unit: metres Time – t  SI unit - s Speed –  SI unit – m/s Vector Position -  SI unit: metres Displacement –  SI unit – metres (m) (c) McGraw Hill Ryerson 2007 ∆d∆d ﺤ

What is velocity? Velocity ( ) 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. (c) McGraw Hill Ryerson 2007

Velocity 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). (c) McGraw Hill Ryerson 2007

Remember this slide from 8.1 Scalar Distance - d  SI unit: metres Time – t  SI unit - s Speed –  SI unit – m/s Vector Position -  SI unit: metres Displacement – SI unit – metres (m) Velocity –  SI unit – m/s (c) McGraw Hill Ryerson 2007 ∆d∆d ﺤ

Same Speed, different Velocities (c) McGraw Hill Ryerson 2007 These two ski gondolas have the same speed but have different velocities.

Question But why do the two gondolas have different velocities? (c) McGraw Hill Ryerson 2007

Lets look at the definitions again. Speed ( ) is the distance an object travels during a given time interval divided by the time interval. Velocity ( )is the displacement of an object during a time interval divided by the time interval. (c) McGraw Hill Ryerson 2007

Remember the definitions of distance and displacement! Distance ( d ) is a scalar quantity that describes the length of a path between two points or locations. Displacement describes the straight-line distance and direction from one point to another. (c) McGraw Hill Ryerson 2007

Here we see the difference (c) McGraw Hill Ryerson 2007

Therefore: The two gondolas are travelling at the same speed. But they are traveling in opposite directions One of the two directions must be given a negative sign Therefore, they have different velocities Clip (c) McGraw Hill Ryerson 2007

Calculating the slope of a position-time graph Dash and a Cheetah are seen in a race below (motion diagram). Each is running at a constant velocity. (c) McGraw Hill Ryerson 2007

During equal time intervals, the position of Dash changes more than the position of the Cheetah. Since, Dash’s displacement for equal time intervals is greater than the Cheetahs Dash is running faster than the Cheetah. (c) McGraw Hill Ryerson 2007

Question How can we calculate how fast Dash and the Cheetah are moving? (c) McGraw Hill Ryerson 2007

We need to know the displacement and the time interval. The motion diagram can be placed on a position-time graph.  Which represents the motion of objects  We can determine the velocity of the objects from the graph (c) McGraw Hill Ryerson 2007

Does Dash or the Cheetah’s motion have the greater slope? Which one is running faster? (c) McGraw Hill Ryerson 2007 Dash Cheetah

(c) McGraw Hill Ryerson 2007 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. Dash Cheetah X-axis Y-axis

Calculating the Slope of the Position-Time Graph On a position-time graph the slope is the change in position (displacement) ( ) divided by the change in time ( ). The steeper the slope the greater the change in displacement during the same time interval. (c) McGraw Hill Ryerson 2007

Dash Cheetah

Lets calculate and compare the slopes of Dash and the Cheetah. Slope = = 2.0 m/s foreword (c) McGraw Hill Ryerson 2007 Dash Cheetah Slope = = 4.0 m/s foreword

Average Velocity Compare the two slopes:  Dash – 4.0 m/s  Sonic – 2.0 m/s Is the slope related to the runners speed based on this information? (c) McGraw Hill Ryerson 2007 Faster

Lets find out. Look at the units m/s The slope shows on average how many metres Dash and the Cheetah moved in 1 second Therefore, the slope of a position-time graph for an object is the object’s average velocity. (c) McGraw Hill Ryerson 2007

Average Velocity Average velocity is the rate of change in position for a time interval. The symbol of average velocity is: Average velocity is a vector and includes a direction. See pages

Question Do you remember what type of slopes a position-time graph can contain?  Positive  Zero  Negative (c) McGraw Hill Ryerson 2007

Position-time graphs and average velocity On a position-time graph, if forward is given a positive direction:  A positive slope means that the object’s average velocity is forward. (c) McGraw Hill Ryerson 2007

Position-time graphs and average velocity On a position-time graph, if forward is given a positive direction: Zero slope means the object’s average velocity is zero. (c) McGraw Hill Ryerson 2007 Which means the object is stationary!

Position-time graphs and average velocity On a position-time graph, if forward is given a positive direction:  A negative slope means that the object’s average velocity is backward. (c) McGraw Hill Ryerson 2007

Review (c) McGraw Hill Ryerson 2007 Time Intervalt1- 0t2 –t1t3 – t2 Velocity Motion Returning to the origin at a uniform speed. Moving away from the origin at a uniform speed Negative zero Positive Remaining stationary

Note: Since the slope of a position-time graph is the average velocity we can use this relationship to calculate the average velocity without analyzing a position-time graph. (c) McGraw Hill Ryerson 2007

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? 1.A boat travels 280 m east in a time of 120 s. What is the boat’s average velocity? See page m/s forward 2.3 m/s East

More to come tomorrow. (c) McGraw Hill Ryerson 2007

Finishing off 8.2 TUESDAY APRIL 22 nd Clip (c) McGraw Hill Ryerson 2007

Remember from last day Average velocity is the rate of change in position for a time interval. The symbol of average velocity is: Average velocity is a vector and includes a direction. See pages

Remember The relationship between average velocity, displacement, and time is given by: So we can rearrange this equation to find displacement. (c) McGraw Hill Ryerson 2007

Question What is displacement? Displacement describes the straight-line distance and direction from one point to another. (c) McGraw Hill Ryerson 2007

Calculating Displacement The relationship between displacement, average velocity, and time is given by: See page 369

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? 2.A person, originally at the starting line, runs west at 6.5 m/s. What is the runner’s displacement after 12 s? (c) McGraw Hill Ryerson m [N] 78 m [W]

Finding time! To find time, the equation can be rewritten again. So, from We can now write the above (c) McGraw Hill Ryerson 2007

Calculating Time The relationship between time, average velocity, and displacement is given by: See page 369

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? 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? (c) McGraw Hill Ryerson s 0.73 s

Converting between m/s and km/h How would you convert velocity in km/h to m/s? 1.Change kilometres to metres: 1000m = 1 km or 1 km = 1000 m 2.Hours to seconds: 3600 s = 1 h or 1 h = 3600 s (c) McGraw Hill Ryerson 2007 Speed zone limits are stated in kilometres per hour (km/h).

(c) McGraw Hill Ryerson 2007 Converting between m/s and km/h Multiply by 1000 and divide by 3600 or Divide the speed in km/h by 3.6 to obtain the speed in m/s. See page 369

Example: For example, convert 75 km/h to m/s. (c) McGraw Hill Ryerson 2007

Example 55 km/h [W]? (c) McGraw Hill Ryerson 2007 = 15 m/s [W]

(c) McGraw Hill Ryerson 2007 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? See page m/s 35 km/h [N], 9.6 m/s [N ] 40 km [E] or 40, 000 m [E]

End of Chapter 8 (c) McGraw Hill Ryerson 2007