Bellringer

Compare and explain in complete sentences what

are velocity, speed and acceleration vs time.

Previous homework

WRITE DOWN THE PROGRESS REPORT

ON YOUR SCIENCE PROJECT: WHAT YOU

ALREADY DID AND YOU PLAN TO DO

Current Homework

Graph your motion: distance, velocity, and

acceleration for your travel on a bus/car

from home to school and back

Graphing Motion

Every Picture Tells A Story

Read and interpret motion graphs

Construct and draw motion graphs

Determine speed, velocity and accleration

from motion graphs

If you make a graph by hand it should always be on graph paper.

The graph should fill theavailable space. Carefullychoosing the best scale isnecessary to achieve this.

The graph should alwayshave a title.

Always label the x and y axes in 3 ways: title, numerical values, and units.

Always make a line graph line graphs are way more handy, because they tell you how one thing changes under the influence of some other variable. 

X axisThe x axis is always the independent variable.

If time is one of the measurements being graphed, it always goes on the x-axis.Independent Variable or Manipulated Variable is what you are testing. It is what causes things to change as you make changes to it. Some people nickname it the I-do variable.

The y axis is always the dependent variable.

Y axis

Dependent Variable or the Responding Variable is the effect and it may or may not change. It is observed during as well as at the end of the experiment.

Dependent Responing Y-axisManipulated Independent X-axis

D = dependent variableR = responding variableY = graph information on the

vertical axis

M = manipulated variable I  = independent variableX  = graph information onthe horizontal axis

Example of a Bad Graph

There's no title.  What's it a graph of?  Who knows?

There are no labels on the x or y axis.  What are those numbers?  Who knows?

There are no units on the x or y axis.  Is this a graph of speedin miles per hour or a graph of temperature in Kelvins?  Who can tell?

What’s wrong with this graph?

There's no title. What's it a graph of? Who knows?

There are no increments on the axes, and there are no gridlines.

There are no labels on the x or y axis. What are those numbers?Who knows?

There are no units on the x or y axis. What size are the numbers: kilo-, centi-, or milli- ?

Numerical measure of a line's incline relative to thehorizontal.

In analytic geometry, the slope ofany line, ray, or line segmentis the ratio of the vertical to thehorizontal distance betweenany two points on it(“slope equals rise over run”).

Definition of slope

Positive slope

Zero slope

Negative slope

Velocity is positive when theobject moves in the positivedirection. Since the positionvalue is increasing, the graphslopes upward.

Velocity is zero when the positiondoes not change. This line haszero slope.

Velocity is negative when theobject moves In the negativedirection on the Axis system.This line has a negativeSlope.

A displacement – time graph with time along x axis and displacement on the y axis.

Types of Motion Graphs

Distance vs TimePosition vs TimeVelocity vs TimeAcceleration vs Time

Distance vs Time Graphs

Speed is the distance an object travels per unit of time.

You can graphically represent the speed or an object using a distance-time graph.

If the speed is constant, then the slope is constant (straight line).

Constant Speed

A constant speed graph shows a constant & positive slope

A uniform distance is covered for each unit of time.

The steeper the slope, the faster the speed.

If the speed is changing, then the slope is changing (curve).

Describe the motion in each section of the graph.

Decelerating

Accelerating

Stopped

Steady speed

Position vs time Graphs of Constant motion

Position vs. time graphs give you an easy and obvious way of determining an object’s displacement at any given time, and a subtler way of determining that object’s velocity at any given time.

A position-time graph, is one in which position isPlotted on the y-axis and the time is on the x-axis.A position-time graph is similar to a distance-timeGraph but has direction on the y-axis.

Although distance-time and position-time graphs can showSimilar graphs, this is not always the case. Below is a graphof a person who walked to a nearby store (10 km north)and back to the original reference point, this would meanthe total travelled distance is 20 km (10 km to the storeand 10 km back). The distance-time graph is on the left.

The position-time graph looks different because the position changed when the person turned back from thestore back to the original reference point.

Looking at the slope of a distance vs time or a position vs time graph...

Slope = Velocity

As slope goes, so does velocity.”

•If the speed is constant, then the slope is constant (straight line).

•If the speed is changing, then the slope is changing (curve).

•If the velocity is positive, then the slope is positive (moving upward, towards the right).

•If the velocity is negative, then the slope is negative (moving downward, towards the right).

•The steeper the line/curve, the faster the speed.

Reading and interpreting position-Time graphs

s vs t - The object is standing still at a positive location.

Time is going by but the position is not changing.

Since the slope equals zero it has no movement.

s vs t - the object is traveling at a constant positive velocity.

The locations of its position are increasingly positive.

s vs t - the object is traveling at a constant positive velocity but is traveling through a negative region.

s vs t - this slope represents a constant negative velocity since the object is traveling in a negative direction at a constant rate.

Notice that the locations of its position are becoming less and less positive

s vs t - the object is traveling at a constant negative velocity through a negative region.

The locations of its position are increasingly negative.

The meaning of slope on a position-timegraph!

If calculated properly, it shows the velocity of the motion.

In this graph Car A movesfor 5 seconds a distance of 10 meters.

How can we figure out thevelocity of the car fromthe graph?

We can use the formula forthe slope of a line to getthe velocity.

Any point on this graph shows the position of the ant at a particular moment in time.

The point at (2,–2) show that, two seconds after it started moving, the ant was two centimeters to the left of its starting position.

The point at (3,1) shows that, three seconds after it started moving, the ant is one centimeter to the right of its starting position.

For the first two seconds, the ant is moving to the left.

The next second, it reverses its direction and moves quickly to y = 1 .

The ant then stays still for three seconds before it turns left again and moves back to where it started.

For any position vs. time graph, the velocity at time t is equal to the slope of the line at time t.

In a graph made up of straight lines, like the one for the ant, the slope can easily be calculated at each point on the graph to show the instantaneous velocity at any given time.

Determine the ant’s instantaneous velocity at any given point during the trip. Remember the instantaneous velocity shows the velocity of the ant at one point. The ant is cruising along at

the fastest speed between t = 2 and t = 3, because the position vs. time graph is steepest between these points.

Calculate the ant’s average velocity during this time interval is a simple matter of dividing rise by run.

Remember average velocity is the total displacement divided by the total time.

The average velocityhere is zero becausethe total diaplacementis zero.

0/7 = 0 m/s

Stage 1: The car moves forwards from the origin to in the first 5 s.

Calculate the velocity for the car after the first five seconds.

Stage 2: The car moves backwards, passes the origin, to in the next 5 s.

Calculate the velocity of the car between five and ten seconds.

Stage 3: The car remains at rest in the last 5 s.

Calculate the velocity of the car for the last five seconds.

Different Slopes

0

1

2

3

4

5

6

7

8

1 2 3 4 5 6 7

Time (hr)

Dis

tan

ce (

km

)

Run = 1 hr

Run = 1 hr

Run = 1 hr

Rise = 0 km

Rise = 2 km

Rise = 1 km

Slope = Rise/Run= 1 km/1 hr= 1 km/hr

Slope = Rise/Run= 0 km/1 hr= 0 km/hr

Slope = Rise/Run= 2 km/1 hr= 2 km/hr