Ch. 3 & 4 Vectors, Speed, Velocity, & Acceleration In this initial lesson students learn about distance, position, and displacement through the use of an interactive simulation The presentation contains introductory information to help students understand how these variables appear in both graphical formats and in word problems. This lesson considers only one dimensional situations. The next lesson extends these ideas to 2 dimensional systems.

Engaging with the concept What is the difference between distance and position? Distance is always positive. It doesn’t tell you where you are because it has no direction information. Displacement is a change in position that includes direction.

Position Position tells you where you are relative to an origin. Positive and negative values tell you whether you are in front or behind, or to the left or right of the origin. A position value has no meaning if the origin is not clearly understood.

Displacement Displacement is a change in position. Positive and negative values indicate direction. You could also note that d = xf – xi . Displacement equals the change in position.

Displacement is a vector Displacement is a vector because it contains direction information. For motion along a line, direction is positive or negative.

What is a vector? Some quantities in physics include direction information. Can you name any? Any variable in which it makes a difference which direction you go, such as forward or backward, must be a vector. Can they give an example of a variable that is NOT a vector?

Distance is a scalar Distance is a scalar quantity. It does not include direction information.

What is a scalar? Scalars Mass and temperature are scalars because you don’t need a “direction” to understand what their values mean. Time is another very important scalar quantity that they will be using frequently.

Adding displacements An ant starts at 2 m, and crawls forward 7.1 m. Then it turns around and crawls back 5.5 m. What is the ant’s final position? Add displacements graphically by drawing vectors to scale: The first vector starts at the initial position. The second vector starts at the end of the first vector. Reinforce the fact that the second vector starts at the tip (or head) of the first vector.

Adding displacements An ant starts at 2 m, and crawls forward 7.1 m. Then it turns around and crawls back 5.5 m. What is the ant’s final position? You can also use numerical addition. This is faster and more accurate. Reinforce the fact that the second vector starts at the tip (or head) of the first vector.

Assessment Identify each variable listed below as either a vector or a scalar. Are there any variables that are neither vectors nor scalars? weight force displacement length velocity Time The first assessment addresses the first objective: “State the definition and give examples of vector and scalar variables.” The answer appears on the next slide.

Assessment Identify each variable listed below as either a vector or a scalar. Are there any variables that are neither vectors nor scalars? weight vector force vector displacement vector length scalar velocity vector time scalar All variables used in this course are either vectors or scalars. In this course all variables are vectors or scalars. In more advanced work other types of variables (such as phasors) may be required.

Assessment A boat travels 5 kilometers east, then 8 kilometers north, and then 8 kilometers west. How would you calculate the boat’s displacement? How would you calculate the boat’s distance? (-8, 0) km (0, 8) km (5, 0) km

Speed versus velocity Are speed and velocity just two different words for the same thing? In everyday life you probably use the words speed and velocity interchangeably. In physics class, speed and velocity are related, but not exactly the same. Ask students to use the words speed or velocity in a sentence.

Equations s The speed is the distance traveled divided by the time taken. speed is always positive! The velocity is the change in position divided (displacement) by the change in time. Moving forward is a positive velocity. Moving backward is a negative velocity.

Brainstorm: An accelerating object has a changing velocity. Can you share an example of something accelerating?

Examples a coaster making a turn a ball rolling uphill a baseball falling

What is acceleration? 4 m/s 4 m/s 4 m/s 4 m/s Two balls are moving to the right. Their velocity at each second is shown. Which ball is accelerating? What is its acceleration? Ball 1 0 m/s 4 m/s 2 m/s Ball 2 6 m/s

What is acceleration? 4 m/s 4 m/s 4 m/s 4 m/s Two balls are moving to the right. Their velocity at each second is shown. Which ball is accelerating? What is its acceleration? Ball 2 is accelerating at +2 m/s per second: a = +2 m/s2 Ball 1 0 m/s 4 m/s 2 m/s Ball 2 6 m/s

The meaning of acceleration Acceleration is the rate at which velocity changes. a = acceleration (m/s2) Δv = change in velocity (m/s) Δt = change in time (s)

Units of acceleration The acceleration tells you how many meters per second your velocity changes in each second. These units are usually written as meters per second squared.

What is free fall? An object is in free fall whenever it moves solely under the influence of gravity, regardless of its direction. A ball falling down, with negligible air resistance A ball thrown up, with negligible air resistance A ball launched at ANY angle, as long as there is negligible air resistance

Gravity and free fall Near Earth’s surface, free-falling objects have a downward acceleration of 9.8 m/s2. If an object is dropped from rest, then . . . after 1 second its velocity is -9.8 m/s. after 2 seconds its velocity is -19.6 m/s. after 3 seconds its velocity is __?___ after 10 seconds its velocity is __?___

Gravity and free fall Near Earth’s surface, free-falling objects have a downward acceleration of 9.8 m/s2. If an object is dropped from rest, then . . . after 1 second its velocity is -9.8 m/s. after 2 seconds its velocity is -19.6 m/s. after 3 seconds its velocity is -29.4 m/s. after 10 seconds its velocity is -98 m/s.