Displacement and Velocity

p. 40-46

Objectives

The student will be able to:

• Describe motion in terms of displacement, time, and velocity

• Calculate the displacement of an object traveling at a known velocity for a specific time interval

• Construct and interpret graphs of position versus time

Displacement

Displacement: the straight-line change in position of an object

• Units: meters (m)

• Symbol: Δx

When an object is at rest, its displacement is zero because its position does not change.

Displacement vs. Distance

• If you were to describe the trip from your home to school, you would describe all the twists and turns in your journey.

• However, the displacement is the same no matter what route you take to school.

• Any path connecting your house and the school will result in the same displacement.

What’s the football player’s displacement?

What’s the football player’s distance traveled?

Trying out Socrative for 1st Time

Poll will go here – conceptual challenge ?’s from p.41

Coordinate Systems

Coordinate System: a system the uses coordinates to establish position

• In this second chapter, we will be working in one dimension, which means we'll only be measuring in one direction (left and right, up and down, north and south, etc.)

Displacement Equation

Δx = xf - xi

• The values xf and xi represent the final position and initial position.

• The xf and xi are determined by their positions on the coordinate system.

Negative and Positive

• Displacement can be positive or negative.

• Displacement is an example of a quantity that has both a magnitude (size) and a direction.

• The direction of the displacement is designated by the sign (positive or negative.)

• We will say that displacements to the left and down are negative and displacements to the right and up are positive.

Average Velocity

Average Velocity: total displacement divided by the time interval during which the displacement occurred

• Units: meters/second (m/s)

• Symbol: or vavg

Velocity Equation

Like displacement, velocity has a magnitude and a direction.  The sign of the displacement indicates direction.  

An object traveling to the left or down has a negative velocity, and an object travelling to the right or up has a positive velocity.

=

Velocity vs. Speed

Velocity indicates how fast something is traveling, and the direction in which it is traveling.  

Speed, however, has no associated direction.

The average velocity depends on displacement, but the average speed is equal to the distance traveled divided by the time interval.

Sample Problem 2A

p.43 – During a race on level ground, Andra covers 825 m in 137 s while running due west.

Find Andra’s average velocity.

Practice Problems

Practice 2A – p.44 #1-4

Quick Note on Average Velocity

• Average velocity is not always equal to the average of the initial and final velocities.

• For instance, if you drive first at 40 km/h west and later at 60 km/h west, your average velocity is not necessarily at 50 km/h west.

Graphing Velocity

On a position versus time graph, the slope of the line connecting one point and the next indicates the average velocity.

slope

Describe the velocity of each object.

Instantaneous Velocity

• For an object that is not traveling at constant velocity, the average velocity will depend on the time interval we choose.

• To find the velocity of the object at a certain instant of time, we study a small time interval near that instant. As the intervals become smaller and smaller, the vavg approaches the exact velocity at that time.

Instantaneous Velocity

Instantaneous velocity: velocity of an object at some instant or at a specific point in the object’s path.

You can determine the instantaneous velocity for a position vs. time graph by drawing a straight line that is tangent to your graph at that instant. The slope of your tangent line is the instantaneous velocity.

Homework

p. 69-70 # 1, 2, 6, 9-11