Acceleration Notes
What is Acceleration? Objects that have motion change direction and speed. Any time a change occurs, it is a change in velocity. The rate at which velocity changes is called acceleration. The units for acceleration are meters per second per second OR m/s2.
Acceleration as a Vector Acceleration is also a vector (has magnitude and direction) Most often we use the word acceleration to describe an object that is increasing in speed. Scientifically though, acceleration applies to any change in any objects speed. Even when an object is slowing down it is accelerating.
4 Ways to Accelerate 1. Speed up 2. Slow down 3. Turn 4. Stop
Example 1 Joshua runs laps at the track at a constant speed. Joshua therefore has no acceleration. As Joshua slows down to grab a drink of water, his speed decreases (negative acceleration known as deceleration ). His acceleration is decreasing. Deceleration is an acceleration that slows an objects speed.
Example 2 As you ride a Ferris wheel you are moving at a constant speed but also are changing direction. This change in direction means that you are accelerating. Any changes an object has in direction, even if it is not changing speed, is also changing acceleration.
Example 3 Some objects, like roller coasters, constantly change speed and direction. The passengers experience constantly changing acceleration. a constant acceleration is a steady change in velocity. Each second the velocity changes by the same amount.
Calculating Acceleration We can calculate acceleration for straight-line motion by dividing the change in velocity by the total time Acceleration = change in velocity/total time a = (vf-vi)/t a= acceleration (m/s2) vf= final velocity (m/s) vi= initial (starting) velocity (m/s) t = time (s)
How to Determine Velocity? Hmm… Describe the changing velocity of a basketball thrown up in the air. When does the basketball have zero velocity? What is the starting velocity of a car that is stopped at a stop sign? What is the final velocity of a car that is coming to a stop? The basketball has a velocity of zero right before it falls. 0 m/s 0 m/s
If dropped from the same height at the same time in a vacuum, which will hit the ground first… A feather Or a bowling ball
http://www.youtube.com/watch?v=AYz_K3mwq6A&feature=related
Free Fall Objects An object that is free falling (near earth) due to gravity has an increase in velocity of 9.8 m/s2 (meters per second squared) for every second it falls. We will say the acceleration is 10 m/s*s.
Free Fall Examples 9.8 m/s2 9.8 m/s2 What is the acceleration of a feather that is falling from a bird’s nest? What is the acceleration of a bowling ball dropped from the same distance? 9.8 m/s2 9.8 m/s2
Calculation Example 1 A car rolls from the top of a hill, starting from rest. After 5 seconds, its velocity is 15 meters per second. What is the acceleration of the car? S: (15 m/s – 0 m/s)/5 s S: 3m/s2 down the hill G: U: E: t= 5 s a=? (vf-vi)/t vi: 0 m/s vf: 15 m/s
Calculation Example What is the acceleration of a vehicle that changes its velocity from 500 m/s to a dead stop in 10 s?
Calculating Example 3 When the shuttle bus comes to a sudden stop to avoid hitting a dog, it accelerates uniformly at 4.1m/s2 as it slows from 9.0 m/s to 0 m/s. Find the time interval of acceleration for the bus. G: U: E: a= -4.1 m/s2 t=? t = (vf-vi)/a Vi= 9.0 m/s Vf= 0 m/s S: t= (0-9)/-4.1 S: time = 2.2 s
Calculation Example 4 An object starts from rest and falls freely under the force of gravity. What is its velocity at the end of 22 seconds? S: vf= 10x22 S: vf = 220 m/s down G: U: E: t= 22 s vf=? Vf=a*t vi=0 m/s a=10 m/s2
Graphing Acceleration The slope of a speed-time graph tells you the acceleration!
Speed-Time Graphs Speed-Time Graphs look much like Distance-Time Graphs. BE SURE TO READ THE LABELS!! Time is plotted on the x-axis. Speed or Velocity is plotted on the Y-axis! A straight horizontal line on a speed-time graph means that speed is constant. It is not changing over time. *A straight line does NOT mean that the object is not changing over time! Object moving at Constant Speed/velocity
Speed-Time Graphs This graph shows speed is increasing. The moving object is accelerating! Object is Accelerating
Speed-Time Graphs This graph shows that speed is decreasing. The moving object is decelerating! Object is Decelerating
Speed-Time Graphs Both the dashed and solid line show increasing speed. Both lines reach the same stop speed, but the solid one takes longer. The dashed line shows a greater acceleration. Steeper slope = greater acceleration
1. In which sections of the graph is Goofy traveling at a constant velocity? What are these velocities? ______________________________________ 2. In which sections of the graph is Goofy accelerating? ________________ 3. In which sections of the graph is Goofy decelerating? ________________
4. Goofy is traveling with the greatest velocity between seconds _______________ 5. Goofy is traveling with the lowest velocity between seconds ____________ 6. Which section shows Goofy’s greatest acceleration? __________________
7. Which section shows Goofy’s greatest deceleration 8. What would the line graph look like if Goofy was stopped?
9. Which section shows Goofy’s greatest deceleration 10. What would the line graph look like if Goofy was stopped?
11. Calculate Goofy’s acceleration in Section A. Show your work. 12. Calculate Goofy’s acceleration in Section B. Show your work. 13. Calculate Goofy’s acceleration in Section C. Show your work.