 # Graphing Motion Position vs. Time Stationary objects

## Presentation on theme: "Graphing Motion Position vs. Time Stationary objects"— Presentation transcript:

Graphing Motion Position vs. Time Stationary objects
Position is same at every time (d = 0) So speed = 0 Stationary objects

Graphing Motion Objects with constant speed
Position t Position changes same amount every interval If it moves 2m in 1st second, it will move 2m every second Objects with constant speed

Graphing Motion Objects with constant velocity
Position t The slope is the change in position/ change in time That’s the speed or velocity! KEY FINDING: Slope of position/time graph is the speed or velocity Negative slope: object is moving in the negative direction Objects with constant velocity Change in position Change in time

Interpreting Graphs What’s going on here?
Starts in a positive position Moves forward with constant speed Stops for a while Goes backward with constant speed Goes forward with constant speed to the origin (x = 0) What’s going on here? Position t

Graphing Speed vs. Time For constant speed (could be sitting still, could be moving), speed doesn’t change Graph is just a flat line REMEMBER: This is just the slope of the position/time graph! Position Speed Case 2: Positive Constant Speed Case 2: Positive Constant Velocity Case 1: No Motion Case 1: No Motion t t

Area under the curve Question: What does the area under the Velocity vs. Time graph tell you? 4 3 2 1 Speed (m/s) Time (s) Answer: velocity x time = distance

Area under the curve It works for changing velocity, too!
4 3 2 1 Speed (m/s) Time (s) What is the total displacement? Area of the triangle: ½ * 4 * 4 = 8 meters

What’s happening here? We call it Acceleration
Getting faster and faster Slope increases, therefore… Speed increases We call it Acceleration Speed t Position t

Acceleration Notes Acceleration is any change in speed or direction.
Acceleration occurs when an object speeds up, slows down (or changes direction– we’ll see this later)

Acceleration Notes Uniform (or constant) acceleration: when an object accelerates at a constant rate over a period of time. Acceleration = change in velocity/time interval Speed t

Acceleration Notes Mathematically: a = Δv = “change in velocity” v = final velocity vo = initial velocity Units: (m/s) or m s s2 Δv = v -vo t t

Acceleration Notes Example: A car starts out traveling at 10 m/s and accelerates to 19 m/s in a time of 3 seconds. What is the acceleration of the car? a = vf –vi = 19 m/s – 10 m/s = 3 m/s t 3s The car accelerates at 3 m/s2.

Finding Acceleration on a Velocity Graph
For linear change in velocity, acceleration is the slope of the velocity graph Positive slope, so positive acceleration Speed Slope = accel = 0 Negative slope, so neg. acceleration (sometimes called “deceleration” t

Average Speed If the speed is changing linearly (constant acceleration) Average speed is just the average of the initial and final speeds vave = v + vo t V Vave Vo

Average Speed: Careful!
If I accelerate uniformly from 10 to 20 mph (miles per hour), what’s my average speed? Constant acceleration: ½ * ( ) = 15 mph If I drive 10 mph for 10 miles and 20 mph for 10 miles, what’s my average speed? 13.3 mph! Not constant acceleration, so not 15 mph!!!