Scalar and Vector Quantities

1. Scalar and Vector Quantities • A scalar quantity is one that only indicates “ how much” ( the magnitude) of the quantity. • A vector quantity indicates the “ how much” ( the magnitude) AND the direction of the quantity. A vector quantity is written with an arrow ( ) above the quantity.

2. Vector directions; When working with vectors (especially adding vectors), we need to know how to represent the direction. Our textbook looks at 2 different methods (see pages 139 and 140). • X – axis method [up] and [right] are positive [down] and [left] are negative Other directions are given in degrees from the right axis (x-axis) in a counter clockwise direction. • Navigator method (compass) [N] and [E] are positive [S] and [W] are negative Other directions are given in degrees from [N] in a clockwise direction

3. Distance and Displacement • Distance is a measurement of the change in distance of an object moving from a starting reference point. Distance is a scalar quantity. Example: ∆d = 5 m • Displacement is a measurement of the change in distance and the direction or the change in position of an object from a reference point. Example: ∆d = 5 m [right]

4. Speed and Velocity • Speed describes the rate of motion of an object. Speed is a scalar quantity. Example: v = 100 km/hr • Velocity describes both the rate of motion and the direction of an object, so velocity is a vector quantity. Example: v = 100 km/hr [E]

5. Velocity is a vector quantity, so you must state its magnitude and direction. Average velocity = displacement time v = ∆d ∆t v = dfinal - dinitial tfinal - tinitial The units for velocity are the same as speed; metres/second (m/s) but you ALSO include a direction in square brackets behind the units given. Example; 10m/s [west]

6. Example Problem B1.6 page 141 Practice Problems #8, 9, 10 page 141

7. Using Graphs to Analyze Average Velocity NOTES provided. • Position-time graph  Is similar to distance-time graph (determining average speed by slope of the line) except that velocity and position (displacement) are vector quantities and must be stated in terms of magnitude and direction  Average velocity = slope • Velocity-time graph  Is similar to speed-time graph (determining distance by calculating area under the line) except that velocity is a vector quantity and must be stated in terms of magnitude and direction  Area = ∆v x t

8. Check and Reflect page 145 #1, 2, 3, 4, 5, 6