Lesson 1 – Speed and Velocity in One and Two Dimensions

Minds-On *this slide isn’t intended to be shown in class The minds-on activity can involve the teacher skateboarding or rollerblading in one direction across the classroom while tossing a ball in the air and catching it. Then ask the students, how fast is the ball travelling in the horizontal direction? The idea to get across is that the velocity of the ball is relative. To a stationary reference point, the ball is moving at the same velocity as the teacher. To the teacher, it is not moving at all in the horizontal direction.

Motion in One Dimension Also called Linear Motion Can occur on a horizontal plane, a vertical plane, or an incline plane (a plane at an angle to the ground) When describing motion in one dimension, we use a Scalar A Scalar is a quantity that is fully described by a magnitude (or numerical value) alone

Example of Scalar Quantities

Instantaneous vs. Average Speed  At a race track like the one shown above, the instantaneous speed of the cars driving is always changing. The speed at any given instant is called the instantaneous speed.

Instantaneous vs. Average Speed

Motion in Two Dimensions Because objects in the real world move in more than one dimension, we need quantities which can describe motion through more than one dimension When describing motion in more than one dimension, we use a vector A vector is a quantity that is fully described by a magnitude (or numerical value) and a direction

Example of Vector Quantities

Position

Position and Displacement

Think About It What is the distance and the displacement (in miles) of the race car drivers in the Indy 500?

Parameters Cars drive 200 laps in the race Each lap covers 2.5 miles Clickers: DistanceDisplacement a.0 miles b.2.5 miles c.200 miles d.500 miles

Velocity A vector quantity involving position and time is called velocity Velocity can be quantified in two ways similar to speed: instantaneous and average velocity Instantaneous velocity is the velocity at a given moment of time Average velocity is the velocity averaged over a period of time

Velocity

Average Velocity

Graphing Position vs. Time Time t (s)

Slope

The slope of a position-time graph of an object is the velocity of that object

Vector Addition In order to add two vectors together, we first place them head to tail The order does not matter. We can draw vector b first and then a and still get the same result

Vector Addition Let’s add two vectors together

Vector Addition Put the two vectors head-to-tail and draw a third vector from the start of the first one to the end of the second.

Vector Addition

60˚

Vector Addition 45˚

Vector Addition Thus, angle AB = 60˚ + 45˚ = 105˚

Vector Addition

Using the Cosine Law

Using the Sine Law

Finding Angle AR

Finding Angle R

Vector Addition +=

Another Vector Addition Method We can also add vectors using a different method We can add the x-components and y-components of the 2 vectors together to get the resultant vector

Add the X-components X-components: The resultant vector’s x-component magnitude is = 24.4

Y-components Y-components: The resultant vector’s y-component magnitude is 10 + (-7.07) = 2.93

Exit Ticket What is the difference between a scalar and a vector? What is the difference between speed and velocity? Explain why a race car on an oval track travels a different distance vs. displacement.

Homework Nelsen Physics 12 Textbook (2001): Questions 2, 4, 6, 8, 10, 15, 18