Topic:Position-Time

GraphsUnit 1: Chapter 1 and 2

What do patterns in data show us?

• Patterns in data allow us to see relationships between variables

• Graphing data provides a visual image of the relationships between variables in a set of data

Strong pattern = Strong relationship Weak/no pattern = no relationship

How do graphs show strong and weak relationships? • Strong relationship• Small change in one variable

makes a big change in another

• Weak relationship• Changes in one variable has little

to no effect on the other variable

How do we represent motion with a graph?• The motion of an object can be

represented by a position-time graph

• Definition:• Position-time graphs show where things

are at different times

• X-axis:• Represents time

• Y-axis:• Represents position relative to the

starting point

Why are position-time graphs useful?• Suppose you take a car trip that includes 1.5 hours of driving and a half-

hour rest stop, for a total time of 2 hours. You drive a total distance of 90 miles in a straight line. What is your average speed?• 90 miles/2hours = 45mph

• Did you really drive for 2 hours without stopping?• No

• You really covered the 90 miles in 1.5 hours at a speed of 60mph and stopped (with zero speed) for a half hour

Figuring out velocity from a position-time graph• In a position-time graph the velocity of an object can be calculated

using the slope of the graph line

• Steeper line = greater slope = faster the object’s motion

• Slope = average velocity of the object

How do you calculate slope?

• Slope equation

• Using the slope equation:• Pick two points on the line and determine their coordinates• Determine the difference in y-coordinates of these two points (rise)• Determine the difference in x-coordinates of these two pointes (run)• Divide the difference in y-coordinates by the difference in x-coordinates