2.2 Acceleration
description
Transcript of 2.2 Acceleration
![Page 1: 2.2 Acceleration](https://reader034.fdocuments.in/reader034/viewer/2022042518/55397d35550346f02f8b4a37/html5/thumbnails/1.jpg)
Acceleration
p. 48-58
![Page 2: 2.2 Acceleration](https://reader034.fdocuments.in/reader034/viewer/2022042518/55397d35550346f02f8b4a37/html5/thumbnails/2.jpg)
Objectives
The student will be able to:
• Describe motion in terms of changing velocity
• Compare graphical representations of accelerated and non-accelerated motions
• Apply kinematic equations to calculate distance, time, or velocity under conditions of constant acceleration
![Page 3: 2.2 Acceleration](https://reader034.fdocuments.in/reader034/viewer/2022042518/55397d35550346f02f8b4a37/html5/thumbnails/3.jpg)
Acceleration
Acceleration: the rate of change of velocity
• Units: meters per second per second or meters per second squared (m/s2)
• Symbol: a
![Page 4: 2.2 Acceleration](https://reader034.fdocuments.in/reader034/viewer/2022042518/55397d35550346f02f8b4a37/html5/thumbnails/4.jpg)
Average Acceleration Equation
average acceleration =
• Acceleration has both direction and magnitude.
![Page 5: 2.2 Acceleration](https://reader034.fdocuments.in/reader034/viewer/2022042518/55397d35550346f02f8b4a37/html5/thumbnails/5.jpg)
Sample Problem 2B – p.49
As a shuttle bus comes to a normal stop, it slows down from 9.00 m/s to 0.00 m/s in 5.00s.
Find the average acceleration of the bus.
![Page 6: 2.2 Acceleration](https://reader034.fdocuments.in/reader034/viewer/2022042518/55397d35550346f02f8b4a37/html5/thumbnails/6.jpg)
Problem Tip
Watch for implied data in problem statements, such as “starts at rest” (vi = 0 m/s) or “comes to rest” (vf = 0 m/s)
![Page 7: 2.2 Acceleration](https://reader034.fdocuments.in/reader034/viewer/2022042518/55397d35550346f02f8b4a37/html5/thumbnails/7.jpg)
Practice 2B Problems
p.49 #1, 3-5
![Page 8: 2.2 Acceleration](https://reader034.fdocuments.in/reader034/viewer/2022042518/55397d35550346f02f8b4a37/html5/thumbnails/8.jpg)
The signs of the velocity and acceleration combine to describe an object’s motion.
a Motion
+ + speeding up
_ _ speeding up
+ _ slowing down
_ + slowing down
- or + 0 constant velocity
0 - or + speeding up from rest
0 0 remaining at rest
![Page 9: 2.2 Acceleration](https://reader034.fdocuments.in/reader034/viewer/2022042518/55397d35550346f02f8b4a37/html5/thumbnails/9.jpg)
Graphing Acceleration
On a velocity versus time graph, the slope of the line connecting one point and the next indicates the average acceleration.
slope
![Page 10: 2.2 Acceleration](https://reader034.fdocuments.in/reader034/viewer/2022042518/55397d35550346f02f8b4a37/html5/thumbnails/10.jpg)
Acceleration Graph
Describe the acceleration at points A, B, C.
![Page 11: 2.2 Acceleration](https://reader034.fdocuments.in/reader034/viewer/2022042518/55397d35550346f02f8b4a37/html5/thumbnails/11.jpg)
Think/Pair/Share
Conceptual Challenge on p.50
![Page 12: 2.2 Acceleration](https://reader034.fdocuments.in/reader034/viewer/2022042518/55397d35550346f02f8b4a37/html5/thumbnails/12.jpg)
Constant Acceleration
What is it?
Demo - Walking
![Page 13: 2.2 Acceleration](https://reader034.fdocuments.in/reader034/viewer/2022042518/55397d35550346f02f8b4a37/html5/thumbnails/13.jpg)
Deriving Displacement w/Constant Acceleration
What we know so far..
For objects moving with constant acceleration
avg. velocity =
![Page 14: 2.2 Acceleration](https://reader034.fdocuments.in/reader034/viewer/2022042518/55397d35550346f02f8b4a37/html5/thumbnails/14.jpg)
Deriving Displacement w/Constant Acceleration
![Page 15: 2.2 Acceleration](https://reader034.fdocuments.in/reader034/viewer/2022042518/55397d35550346f02f8b4a37/html5/thumbnails/15.jpg)
Displacement w/Constant Acceleration
displacement = (initial velocity + final velocity)(time interval)
• You will know that acceleration is constant by the phrase “uniform negative/positive acceleration”
![Page 16: 2.2 Acceleration](https://reader034.fdocuments.in/reader034/viewer/2022042518/55397d35550346f02f8b4a37/html5/thumbnails/16.jpg)
Sample Problem 2C– p.53
A race car reaches a speed of 42 m/s. It then begins a uniform negative acceleration, using its parachute and braking system, and comes to rest 5.5 s later.
Find out how far the car moves while stopping.
![Page 17: 2.2 Acceleration](https://reader034.fdocuments.in/reader034/viewer/2022042518/55397d35550346f02f8b4a37/html5/thumbnails/17.jpg)
Practice 2C Problems
p.53 #1, 3-5
![Page 18: 2.2 Acceleration](https://reader034.fdocuments.in/reader034/viewer/2022042518/55397d35550346f02f8b4a37/html5/thumbnails/18.jpg)
Velocity with Constant AccelerationWhat if we don’t know the vf but we still want to calculate displacement…
=
![Page 19: 2.2 Acceleration](https://reader034.fdocuments.in/reader034/viewer/2022042518/55397d35550346f02f8b4a37/html5/thumbnails/19.jpg)
Velocity with Constant Acceleration
final velocity = initial velocity + (acceleration · time interval)
![Page 20: 2.2 Acceleration](https://reader034.fdocuments.in/reader034/viewer/2022042518/55397d35550346f02f8b4a37/html5/thumbnails/20.jpg)
Displacement w/Constant AccelerationWe can combine the previous equations:
and to form
![Page 21: 2.2 Acceleration](https://reader034.fdocuments.in/reader034/viewer/2022042518/55397d35550346f02f8b4a37/html5/thumbnails/21.jpg)
Displacement w/Constant Acceleration
displacement = (initial velocity · time interval) +
acceleration · (time interval)2
![Page 22: 2.2 Acceleration](https://reader034.fdocuments.in/reader034/viewer/2022042518/55397d35550346f02f8b4a37/html5/thumbnails/22.jpg)
Sample Problem 2D – p.55
A plane starting at rest at one end of a runway undergoes a uniform acceleration of 4.8 m/s2 for 15 s before takeoff.
What is its speed at takeoff?
How long must the runway be for the plane to be able to take off?
![Page 23: 2.2 Acceleration](https://reader034.fdocuments.in/reader034/viewer/2022042518/55397d35550346f02f8b4a37/html5/thumbnails/23.jpg)
Practice 2D Problems
p.55 #1-3
![Page 24: 2.2 Acceleration](https://reader034.fdocuments.in/reader034/viewer/2022042518/55397d35550346f02f8b4a37/html5/thumbnails/24.jpg)
So far all equations have required knowing the time interval.
If we don’t know t, we need to rearrange an equation and use substitution.
![Page 25: 2.2 Acceleration](https://reader034.fdocuments.in/reader034/viewer/2022042518/55397d35550346f02f8b4a37/html5/thumbnails/25.jpg)
Rearrange for :
![Page 26: 2.2 Acceleration](https://reader034.fdocuments.in/reader034/viewer/2022042518/55397d35550346f02f8b4a37/html5/thumbnails/26.jpg)
Then substitute into:
![Page 27: 2.2 Acceleration](https://reader034.fdocuments.in/reader034/viewer/2022042518/55397d35550346f02f8b4a37/html5/thumbnails/27.jpg)
Final Velocity After any Displacement
• When you use this equation, you must take the square root of the equation to find the vf.
• The square root can be either positive or negative, you will determine which value is right by reasoning based on the direction of motion.
![Page 28: 2.2 Acceleration](https://reader034.fdocuments.in/reader034/viewer/2022042518/55397d35550346f02f8b4a37/html5/thumbnails/28.jpg)
Sample Problem 2E – p.57
A person pushing a stroller starts from rest, uniformly accelerating at a rate of 0.500 m/s2.
What is the velocity of the stroller after it has traveled 4.75 m?
![Page 29: 2.2 Acceleration](https://reader034.fdocuments.in/reader034/viewer/2022042518/55397d35550346f02f8b4a37/html5/thumbnails/29.jpg)
Practice 2E Problems
p.58 #1,3,5
![Page 30: 2.2 Acceleration](https://reader034.fdocuments.in/reader034/viewer/2022042518/55397d35550346f02f8b4a37/html5/thumbnails/30.jpg)
![Page 31: 2.2 Acceleration](https://reader034.fdocuments.in/reader034/viewer/2022042518/55397d35550346f02f8b4a37/html5/thumbnails/31.jpg)
Homework
p.70-71 #18-25