It’s All About Acceleration

Using Velocity Vectors on Motion Diagrams (Quick Review) © 2015 Pearson Education, Inc.

Using Vectors on Motion Diagrams In two dimensions, an object’s displacement is a vector: The velocity vector is simply the displacement vector multiplied by the scalar 1/Δt. Consequently the velocity vector points in the direction of the displacement. © 2015 Pearson Education, Inc.

Question 1: Finding the velocity of an airplane A small plane is 100 km due east of Denver. After 1 hour of flying at a constant speed in the same direction, it is 200 km due north of Denver. What is the plane’s velocity? © 2015 Pearson Education, Inc.

Accelerated Motion

Acceleration You can feel a difference between uniform (constant) and nonuniform (accelerated) motion. When you move in a nonuniform motion, you feel pushed or pulled. In contrast, when you are in uniform motion and your eyes are closed, you feel as though you are not moving at all.

Acceleration So far, we’ve talked about “how far” and “how fast”…now we want to study “how fast an object is getting faster” The rate at which an object’s velocity changes is called acceleration. Acceleration is measured in m/s/s or m/s2. What is meant by “per”

Acceleration Acceleration: is the rate at which velocity changes over time. An object accelerates if its speed, direction, or both change. Acceleration has direction and magnitude. Thus,acceleration is a vector quantity.

Acceleration Consider the motion diagram below showing the distance between successive positions.

Acceleration Two major indicators of change in velocity. The change in the spacing of the dots and The differences in the lengths of the velocity vectors

Acceleration If an object speeds up, each subsequent velocity vector is longer. If the object slows down, each vector is shorter than the previous one. Both types of motion diagrams give an idea of how an object’s velocity is changing.

Displaying Acceleration on a Motion Diagram To determine the length and direction of an average acceleration vector, subtract two consecutive velocity vectors, as shown below.

Displaying Acceleration on a Motion Diagram Direction: You will have: ∆v = vf - vi = vf + (-vi) Acceleration Vector Always the same as ∆ Magnitude: Then divide by the time interval, ∆t. Remember:

Finding the Acceleration Vector Text: p. 69

Question 2 A particle undergoes acceleration while moving from point 1 to point 2. Which of the choices shows the velocity vector as the object moves away from point 2? Answer: C © 2015 Pearson Education, Inc.

Question 3 The diagram shows three points of a motion diagram. The particle changes direction with no change of speed. What is the acceleration at point 2? Answer: B © 2015 Pearson Education, Inc. 16

Vectors and Circular Motion (More on this later) Cars on a Ferris wheel move at a constant speed but in a continuously changing direction. They are in uniform circular motion. © 2015 Pearson Education, Inc.

Position, Velocity, Acceleration Note: Constant Velocity =No Change in velocity ACCELERATION = 0

Positive and Negative Acceleration When the object’s acceleration is in the same direction as its velocity, the object’s velocity increases. When they are in opposite directions, the velocity decreases. So……..…

Positive and Negative Acceleration

Positive and Negative Acceleration What does this all mean? © 2015 Pearson Education, Inc.