Physical Science
Chapter 4 Section 1
Position, Speed and Velocity
Learning Goals
*Explain the meaning of motion.
*Describe an object’s position relative to a reference point.
*Use the speed formula.
*Tell the difference between speed and velocity.
*Position is a variable given relative to an origin .
*The origin is the place where position equals 0.
*The position of this car at 50 cm describes where the car is relative to the track.
4.1 Position, Speed and Velocity
* Position and distance are similar but not
the same.
*If the car moves a distance of 20 cm to
the right, its new position will be 70 cm
from its origin.
cmcm
Start
What is the car's position?
4.1 Position, Speed and Velocity
* The variable
speed
describes how
quickly something moves.
* To calculate the speed of a moving
object divide the distance it moves
by the time it takes to move.
v
d
4.1 Position, Speed and Velocity
* The units for speed are distance
units over time units.
*This table shows different units
commonly used for speed.
4.1 Average speed
* When you
divide the total
distance of a trip
by the time taken
you get the
average speed
.
* On this driving
trip around
Chicago, the car
traveled and
average of 100
km/h.
4.1 Instantaneous speed
* A speedometer shows a car’s
instantaneous speed
.
*The instantaneous speed is the
actual
speed an object has at any
moment.
Practice Problem:
How far do you go if you drive for
two hours at a speed of 100 km/h?
4.1 Vectors and velocity
*Position uses positive and negative numbers.
*Positive numbers are for positions to the right of the origin and negative numbers are for positions to the left the origin.
4.1 Vectors and velocity
4.1 Vectors and velocity
We use the term velocity to mean speed with direction.
4.1 Keeping track of where you are
Pathfinder is a small robot sent to explore Mars.
It landed on Mars in 1997. Where is Pathfinder now?
* Pathfinder keeps track of its velocity vector and uses a clock.
*Suppose Pathfinder moves forward at 0.2 m/s for 10 seconds.
What is Pathfinder’s velocity?
Suppose Pathfinder goes backward at 0.2 m/s for 4 seconds.
What is Pathfinder’s change in position?
* Each change in position is added up using positive and negative numbers.
4.1 Maps and coordinates
*If Pathfinder was crawling on a straight board, it would have only two choices for direction.
*Out on the surface of Mars, Pathfinder has more choices. *The possible directions include north, east, south, and west, and anything in between.
4.1 Maps and coordinates
* A graph using north−south and east−west axes can accurately show where Pathfinder is.
*This kind of graph
is called a
map
.
*Street maps often
use letters and
numbers for
coordinates.
4.1 Vectors on a map
*Suppose you run east for 10 seconds at a speed of 2 m/s.
*Then you turn and run south at the same speed for 10 more seconds.
Where are you compared to where you started?
4.1 Vectors on a map
To get the answer, you figure out your east −west changes and your north−south changes separately.
4.1 Vectors on a map
*Your first movement has a velocity vector of +2 m/s, west-east (x-axis).
*After 10 seconds your change in position is +20 meters (east on x-axis).
d = v x t d = 2 m/s x 10 s = +20 m
4.1 Vectors on a map
*Your second movement has a velocity vector of −2 m/s north−south (y-axis)
*In 10 seconds you move −20 meters (south is negative on y-axis)
d = 2 m/s x 10 s = -20 m
Practice Problem: A train travels at 100 km/h heading east to reach a town in 4 hours. The train then reverses and heads west at 50 km/h for 4 hours. What is the train’s position now?
Classwork:
*4.1 Section Review
*Pg 86
*1-8
Homework
*Read 4.2
Physical Science
Chapter 4
Section 2
Graphs of Motion
Learning Goals
*Construct and analyze graphs of position
versus time, and speed versus time.
*Recognize and explain how the slope of a
line describes the motion of an object.
*Explain the meaning of constant speed
*Constant speed means the speed stays the same. *An object moving at a constant speed always creates a position vs. time graph that is a straight line.
*The data shows the runner took 10 seconds to run each 50-meter segment.
The slope is the speed!
*You can use position vs. time graphs to compare the motion of different objects.
*The steeper line on a position vs. time graph means a faster speed.
*The slope of a line is the ratio of the “rise” to the “run”
* The steepness of a line is measured by finding its slope.
*Objects rarely move at the same speed for a long period of time.
*A speed vs. time graph is also useful for showing the motion of an object that is speeding up or slowing down.
Positive Slope! Negative Slope!
Calculate the distance that this runner went.
What is the
difference
between these
two speed v.
time graphs?
Classwork
*4.2 Section Review
Homework
*4.2 Calculating Slope From A Graph
*4.2 Analyzing Graphs of Motion With Numbers *4.2 Analyzing Graphs of Motion Without Numbers
*#4 is EC!!!
I will NOT give you class time to work on this
tomorrow. Get as much done today in class and finish the rest at home!!!
Physical Science
Chapter 4 Section 3 Acceleration
Learning Goals * Define acceleration.
*Determine acceleration by mathematical and graphical means.
*Explain the role of acceleration in describing curved motion and objects in free fall
*Acceleration is the rate at which your speed (or velocity) changes.
*If your speed increases by 1 meter per second (m/ s) for each second, then your acceleration is 1 m/s per second.
*Acceleration is easy to spot on a speed vs. time graph.
*Acceleration causes the line to slope up on a speed vs. time graph.
* There is zero acceleration at constant speed
because the speed does not change. * Speed and acceleration are not the same thing.
* You can be moving (non-zero speed) and have no acceleration (think cruise control ).
*You can also be accelerating and not moving!
*A falling object begins accelerating the instant it is released.
*Acceleration describes how quickly speed changes.
*Acceleration is the change in speed divided by the change in time.
Practice Problem
A car accelerates from a stop sign to 450m/s in 10 seconds. What is the cars acceleration?
Practice Problem
A sailboat is sailing on a lake at 2m/s. A strong wind gusts and the boat changes it's velocity to 6m/s. What is the boat's acceleration?
*The word “acceleration” is used for any change in speed, up or down.
* Positive acceleration adds more speed each second. *Things get faster.
*Speed increases over time.
* Negative acceleration subtracts some speed each second.
*Things get slower.
*People sometimes use the word deceleration to describe slowing down.
* The position vs. time graph is a curve when there is acceleration.
*The car covers more distance each second, so the position vs. time graph gets steeper each second.
* When a car is slowing down, the speed decreases so the car covers less distance each second. *The position vs. time graph gets shallower with time.
* An object is in free fall if it is accelerating due to the force of gravity and no other forces are acting on it.
*The letter “g” is used for acceleration due to gravity.
* Acceleration occurs whenever there is a change in speed, direction, or both.
* A car driving around a curve at a constant speed is accelerating because its direction is changing.
*A soccer ball is an example of a projectile. *A projectile is an object moving under the influence of only gravity.
*The path of the ball makes a bowl-shaped curve
called a parabola.
* Circular motion is another type of curved motion. * An object in circular motion has a velocity vector that constantly changes
direction.
Classwork
*4.3 Section Review Homework
