Speed and Velocity in One and Two Dimensions

Speed and Velocity in One and Two Dimensions Linear Motion in One Dimension Linear Motion in Two Dimensions Speed and Other Scalar Quantities Velocity and Other Vector Quantities Position and Displacement Position and Velocity Graphs Tangents and Instantaneous velocities Displacement and Velocity in Two Dimensions • Vector Addition, Cosine Law and Sine Law • •

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Kinematics • The study of motion

Linear Motion in One Dimension • _______ • E. g. – Motion of a train along a straight line – An object, like a ball, falling freely, vertically under gravity – The vertical up and down oscillations of an object suspended from a vertical spring.

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Check Your Understanding Ensure SI Units 1. What is the average speed of a cheetah that sprints 100 meters in 4 seconds? 2. If a …………. 1. If your………….

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Velocity and Other Vector Quantities In slideshow mode, click the image on the left to see how videos are embedded into the lesson • A vector quantity is a quantity with a magnitude and direction. – I. e. Displacement, and velocity – I. e. 20 km/h [E]

Position and Displacement • _______ • Displacement is how far an object is from its starting point Final position – starting position

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Velocity • _____________ • Change of position divided by the time interval for that change

Check Your Understanding A cyclist takes 25. 1 s to cover the displacement of 115 m [E] from d 1 to d 2. (a) Calculate the cyclist’s average velocity. (b) If the cyclist maintains the same average velocity for 1. 00 h, what is the total displacement? (c) If the ………….

Think About It 1. Is it possible for the total distance travelled to equal the magnitude of the displacement? If “no, ” why not? If “yes, ” give an example. 2. 3. Is it possible …………. Is it possible for the magnitude of the displacement to exceed the total distance travelled? If “no, ” why not? If “yes, ” give an example. 4. 5. Can the average …………. A truck driver, reacting quickly to an emergency, applies the brakes. During the driver’s 0. 32 s reaction time, the truck maintains a constant velocity of 27 m/s [fwd]. What is the displacement of the truck during the time the driver takes to react?

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Position and Velocity Graphs – Uniform Motion • For a constant velocity motion (the same velocity is maintained), the position-time graph is a straight line and the velocity-time graph is horizontal. Position-Time Data Position-Time & Velocity-Time Graphs

Check Your Understanding • Describe ………….

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Tangents and Instantaneous velocities • Draw ………….

Check Your Understanding This is the position-time graph for a golf ball rolling along a straight trough which slopes downward from east to west. (a) Describe …………. . (b) Calculate the instantaneous velocity at t = 3. 0 s. (c) Determine …………. Picture has been removed

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Vector Addition, Cosine Law and Sine Law • _______ • Sine Law: • Vector Component Addition: Determine all the sum of the x and y components, create a right triangle and solve the hypotenuse using the Pythagorean Theorem

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Check Your Understanding • In 4. 4 s, a chickadee flies in a horizontal plane from a fence post (P) to a bush (B) and then to a bird feeder (F), as shown below. Find the following: (a) total distance travelled (b) average …………. (c) total displacement (d) average velocity

Homework 1. Determine the vector sum of the displacements Δd 1 = 2. 4 m [32° S of W]; Δd 2 = 1. 6 m [S]; and Δd 3 = 4. 9 m [27° S of E]. 2. A skater on Ottawa’s Rideau Canal travels in a straight line 8. 5 x 102 m [25° N of E] and …………. (a) What is the skater’s displacement? (b) What are the skater’s averages peed and average velocity?