/

Lab Report Due Friday  Any questions on the report?

A Graphs of Motion Update Your TOC

Video  ?v=x2ve5yucNPQ ?v=x2ve5yucNPQ  ?v=ohYQMEhl5Cc ?v=ohYQMEhl5Cc

Parts of a Graph  X-axis  Y-axis  All axes must be labeled with appropriate units, and values.

Position vs. Time  The x-axis is always “time”  The y-axis is always “position/distance”  The slope of the line indicates the velocity of the object.  Slope = (y 2 -y 1 )/(x 2 -x 1 )  d 1 -d 0 /t 1 -t 0  Δd/Δt  Velocity = distance time

Uniform Motion  Uniform motion : equal displacements occurring during continuous equal time periods (constant velocity)  Straight lines on position-time graphs mean uniform motion.

Acceleration/Velocity  Acceleration: rate of which an object changes its speed (changing how fast an object is moving)  An object is accelerating if its speed or direction is changing  A= change in velocity Δv change in time Δt  Velocity is the how fast it’s moving. It is measured in m/s.

Acceleration  If an object is not changing its velocity (how fast it’s moving), then the object is not accelerating. 

Acceleration  The data at the right are representative of a northward-moving accelerating object.  The velocity is changing over the course of time.  In fact, the velocity is changing by a constant amount - 10 m/s - in each second of time.  Anytime an object's velocity is changing, the object is said to be accelerating; it has an acceleration.

Which car or cars (red, green, and/or blue) are undergoing an acceleration? Study each car individually in order to determine the answer. (write it in your NB) If you inspect each car individually, you will more likely notice that only the green and the blue cars accelerate. The red car moves with a constant speed, covering the same distance in each second of the animation. The green and the blue cars are speeding up, thus covering an increasing distance in each second of the animation.

Watch the changing of each car(s) velocities. Which is slower change? Which is a faster change? Which has no change? The red car is moving with a constant velocity The green car has a more gradually changing velocity The blue car has a faster changing velocity

Check with your partner  Talk to your neighbor  Explain to them what speed, velocity, and acceleration are  Write down in your notebook the similarities and the differences Speed Velocity Acceleration

Consider the position-time graph at the right. Each one of the three lines on the position-time graph corresponds to the motion of one of the three cars. Match the appropriate line to the particular color of car.

The red car is moving with a constant velocity and must correspond to object B which has a constant slope. The green and blue cars have a changing velocity and must correspond to lines with a changing slopes - objects A and C. The green car is object C which has a more gradually changing slope than object A (blue car).

Steepness of slope on Position-Time graph  Slope is related to velocity  Steep slope = higher velocity  Shallow slope = less velocity

Positive and Negative Acceleration  increase in speed: positive acceleration  decrease in speed: negative acceleration.

Velocity vs. Time  X-axis is the “time”  Y-axis is the “velocity”  Slope of the line = the acceleration

Velocity vs. Time  Horizontal lines = constant velocity  Sloped line = changing velocity  Steeper = greater change in velocity per second  Negative slope = deceleration

Different Velocity-time graphs Constant velocity? Acceleration? Deceleration?

Different Velocity-time graphs Constant velocity? Acceleration? Deceleration?

Different Velocity-time graphs

Acceleration vs. Time Time is on the x-axis  Acceleration is on the y-axis  Shows how acceleration changes over a period of time.  Often a horizontal line.

Constant Rightward Velocity

Constant Leftward Velocity

Constant Rightward Acceleration

Constant Leftward Acceleration

Leftward Velocity with Rightward Acceleration

Practical Application Velocity/Position/Time equations  Calculation of arrival times/schedules of aircraft/trains (including vectors)  GPS technology (arrival time of signal/distance to satellite)  Military targeting/delivery  Calculation of Mass movement (glaciers/faults)  Ultrasound (speed of sound) (babies/concrete/metals) Sonar (Sound Navigation and Ranging)  Auto accident reconstruction  Explosives (rate of burn/expansion rates/timing with det. cord)

Free Fall  Recognize the meaning of the acceleration due to gravity  Define the magnitude of the acceleration due to gravity as a positive quantity and determine the sign of the acceleration relative to the chosen coordinate system  Use the motion equations to solve problems involving freely falling objects

Freefall  Defined as the motion of an object if the only force acting on it is gravity.  No friction, no air resistance, no drag

Acceleration Due to Gravity  Galileo Galilei recognized about 400 years ago that, to understand the motion of falling objects, the effects of air or water would have to be ignored.  As a result, we will investigate falling, but only as a result of one force, gravity. Galileo Galilei Weknowmemes.com

Galileo’s Ramps  Because gravity causes objects to move very fast, and because the time-keepers available to Galileo were limited, Galileo used ramps with moveable bells to “slow down” falling objects for accurate timing.