Unit B 1.2 Velocity

Velocity Describes both the rate of motion and the direction of an object You can determine the speed of a car by looking at the speedometer To determine the average velocity you need both the speedometer and the direction

Scalar and Vector Quantities Scalar quantity indicates “how much” (the magnitude) of the quantity Vector quantity indicates “how much” (the magnitude) and the direction of the quantity Vector quantities are written with an arrow above the quantity. Speed – v Velocity - v

Distance Travelled Scalar quantity Measurement of the change in distance of an object moving from a starting reference point How far has it travelled ? Total amount travelled The girl has moved 10m from the stop sign, so the distance travelled is written as ∆d = 10m

Displacement Vector quantity Measurement of the change in distance and the direction OR change in position of an object from a reference point To determine the displacement you need to know both the beginning and final position of the person, and the direction of the movement. How far are you from where you started ?

The distance travelled by the girl is ∆d = 5m + 9m = 14m The displacement of the girl relative to the stop sign is ∆d = 5m [right] + -9m [left] = -4m [left]

How to Identify Vector Directions In our previous example the vector directions given are [right] and [left]. Vectors can also refer to compass directions: north, south, east and west. The vector direction is determined using the navigator method

The X-Axis Method Uses a coordinate system with an “x” axis and a “y” axis similar to a graph. Right (0°) Up (90°) Left (180°) Down (270°) [up] and [right] are positive [down] and [left] are negative Directions between the axis lines are given only in degrees and are not given a negative of positive value.

Example Use the x-axis method to determine the directions of the vectors A, B, C and D. Give the magnitude and direction for each vector. 10m 6m 2m 8m 30° 40° Vector B Vector C Vector D Vector A

Solution Vector A = 6m [30°] Vector B = 10m [right] Vector C = -8m [down] Vector D = 2m [230°] Practice Problem 6 page 139

The Navigator Method Uses the directions of north [N], south [S], east [E] and west [W] North is the starting reference point of 0° In the method, directions are stated clockwise from north [N] and [E] are positive [S] and [W] are negative Directions between the axis lines are given only in degrees and are not given positive or negative values N (0°) S (180°) W (270°) E (90°)

Example Use the navigator method to determine the direction of the vectors A, B, C and D. Give the magnitude and direction for each vector 10m 6m 2m 8m 30° 40° Vector B Vector C Vector A

Solution Vector A = 6m [60°] Vector B = 10m [E] Vector C = -8m [S] Vector D = 2m [220°] Practice Problem 7 p. 140 Remember to read the questions carefully to see which method you are supposed to use.

Speed and Velocity Using Formulas to Analyze Average Velocity – Change in position in a specified time Average velocity = displacement time elapsed v = ∆d ∆t d = d 1 + d 2 Velocity is a vector quantity, so you must state its magnitude and direction.

Example A person walks 10.0m [E] away from a bus stop in 5.00s. What is the average velocity of the person? v = ∆d ∆t v = 10.0m [E] 5.00s v = 2.00m/s The person walked at an average velocity of 2.00m/s [E] Practice Problems p. 141

Example A dog runs 20 m [N] chasing a ball and then turns around and runs 15 m [S] towards its owner. It takes the dog 12.5s. What is the average velocity of the dog? v = ∆d ∆t v = 5.0m [N] 5.00sv = 1.00m/s The person walked at an average velocity of 1.0m/s [N]

Using Graphs to Analyze Average Velocity Plotting a Position-Time Graph – Use the slope of the line to determine the average velocity Slope = rise = change in position run change in time Slope = Velocity = ∆d ∆t

Example Draw a position-time graph for the data in the table Using the graph, identify the motion occurring during the first 5 seconds Determine the average velocity during the first 5 seconds Time (s)Position of the Object (m) [N]

Solution

The graph is a straight line so it is showing uniform velocity Average velocity = slope Slope = rise = d f - d i run t f - t i = 50.0 [N] – 0.0m [N] 5.0s – 0.0s = 10m/s [N] Since slope = velocity, the average velocity of the object was 10m/s [N]. Practice Problem 11 p. 143

Homework: read Science 10 p Check and Reflect 1-8