Distance-Time Graph Notes

Graphing an Object’s Motion 8.P.2A.6

Daily Objective 8.P.2A.6 Students will use mathematical thinking to generate graphs that represent the motion of an object’s position and speed as a function of time. By the end of class today, I will be able to… Define what slope, motion, distance, displacement, direction, & distance-time graph Understand how a graph’s slope describes the object’s motion

Motion

Motion occurs when there is a change in position of an object with respect to a reference starting point. ● The final position of an object is determined by measuring the change in position (Motion) and direction of the segments along a trip.

What is Motion A change in position

The following terms are used to describe and determine motion:

Position Position is the location of an object. An object changes position if it moves relative to a reference point (starting point). The change in position is determined by the distance and direction of an objects change in position from the starting point (displacement).

Check Point What is motion? What is position? What is the reference point? Check Point

Distance Vs. Displacement Distance is how far an object travels. Ex: _____ Displacement the distance and direction of an object’s change in position from the starting point (displacement). Ex:_______

Displacement A displacement includes both the distance and a direction. Examples of Displacements: - 10 m north - 23 m left - 15 m down Question: How do you know these are displacements?

Ticket Out the Door/Reinforcement Activity Sheet Block 24 Block 3   What is the beginning position of the bus? ____________ What is the ending position of the bus? ___________ What is the direction of the bus? ______________ What is the distance the bus travelled? _______________ blocks What is the displacement of the bus? ___________________

Displacement Displacement = distance + direction 10 m left So what is the main difference between distance and displacement?

Segment Distance (m) Direction X East Y North Z West  For example, given the following data table, determine the change in the object’s position based on its final position, distance, and direction, from a starting point. Segment Distance (m) Direction X 10 East Y 7 North Z West

Give the distance and Displacement for X, Y, Z from previous chart. Segment Distance Displacement X 10 m 10 m East Y 7 m 7 m North Z 10 m West

Check Point What is distance? Give an example Define displacement? Give an example What is the difference between distance and displacement? Check Point

Check Point How do you find the distance? How do you find the displacement? Check Point

Direction Direction is the line, or path along which something is moving, pointing, or aiming. Direction is measured using a reference point with terms such as up, down, left, right, forward, backward, toward, away from, north, south, east, or west.

Speed Speed does not necessarily mean that something is moving fast. Speed is a measure of how fast something moves a particular distance (for example, meters) over a given amount of time (for example, seconds). Speed does not necessarily mean that something is moving fast.

Check Point Define direction. Give an example of direction What is the difference between speed and velocity? Check Point

What is Slope? Slope is the steepness of a line The constant of proportionality is the same thing as a slope

Why is Slope Important? The slope of a graph tells about an object’s motion Steep slope = quick motion Shallow slope = slow motion

SPEED SLOPE -The slope of the line can tell the relative speed of the object. -When the slope of the line is steep, the speed is faster -When the slope of the line is flatter, the speed is slower. -When the slope of the line is flat, horizontal to the x-axis, the speed is zero (no movement)

Position-Time Graphs A graph used to show a change in an object’s location over time. TIME: the ____Independent_______ variable - is plotted on the x-axis and POSITION/DISTANCE: the ______Dependent__________variable - is plotted on the y-axis.

Check Point What is slope? How is slope used to describe an object’s motion? What is a distance- time graph? Time and distance goes on what axis? Check Point

NAME THAT GRAPH (CONSTANT GRAPH)

DISTANCE-TIME AVERAGE GRAPHS

What does Slope Describe? Slope describes the movement of an object Positive slope means the object is accelerating Negative slope means the object is decelerating No slope means the object is at rest

Check Point What is slope? How is slope used to describe an object’s motion? Check Point

Graph and determine the motion of both objects.

Distance-Time graph This distance-time graph can then be used to describe the speed of the object. For example, the speed of segment A is slower than segment C. The speed of segment B is zero, the object is not moving.

PRACTICE FIND TOTAL DISTANCE AND DISPLACEMENT for both lines

Check Point How do you find the distance? How do you find displacement? How do you find the average speed? Check Point

ACTIVITY Create a position-time graph for your day so far. Make sure to label the key parts of your graph (walking to class, sitting in your desk, etc.) Write at least 5 sentences to describe the story of your day. Be sure to include key vocabulary from today’s lesson. Ex: This morning, I woke up and jumped out of bed. I walked at a fast constant speed to the sink where I brushed my teeth for two minutes. I then walked at a slow speed to the kitchen to make breakfast which took fifteen minutes.