Accelerated Motion

Chapter 3

Physics Principles and Problems

Zitzewitz, Elliot, Haase, Harper, Herzog, Nelson, Nelson, Schuler and

Zorn

McGraw Hill, 2005

Acceleration - rate of change in velocity per unit time.

http://www.free-computer-wallpapers.com/pictures/albums/Car_wallpaper/Nascar_ea_sports500.jpg

http://www.munciefreepress.com/files/images/October%202007%20%20Space%20Shuttle%20Discovery%20Launch%20-%201.preview.jpg

Acceleration = ∆v / ∆t (vf - vi / tf - ti)

• 8m/s - 4m/s = 4m/s = 2m/s2

4s - 2s 2s• Acceleration’s units are distance per time squared• What is the graph of an object that is decelerating?• What is the graph of an object at constant acceleration?

Remember a distance vs time graph of an object that is accelerating is quadratic.

• The rate of velocity is not constant. Since the velocity is changing per unit time so to is the distance traveled.

• What is the distance-time graph of an object that is decelerating?

http://www.gravitywarpdrive.com/General_Relativity_Images/Falling_Ball_Graph_Distance.gif

Using the graph explain the acceleration and position of these 5 runners (assume east is positive).

time (s)

velocity

(m/s)

east

west

A

B

CD

E

The sign of acceleration does not indicate whether or notThe object is speeding up or slowing down (only its direction).

Final Velocity with Average Acceleration

a = ∆v OR ∆v = a ∆t OR vf - vi = a ∆t ∆t

vf = vi + a ∆t

Example 1: A bus that is traveling at 30.0km/hr speeds up at a constant rate of 3.5m/s2. What velocity does it reach 6.8s later?

Example 2: A car slows from 22m/s to 3.0m/s at a constant rate of 2.1m/s2. How many seconds are required before the car is traveling at 3.0m/s?

Position with Average Accelerationdf = di + vitf + 1/2atf

2

Velocity with Constant Accelerationvf

2 = vi2 + 2a(df - di)

• Example 1: Sekazi is learning to ride a bike. His father pushes him with a constant acceleration of 0.50m/s2 for 6.0s, and then Sekazi continues at 3.0m/s for 6.0s before falling. What is Sekazi’s displacement?

• Example 2: Sunee is training for an upcoming 5.0km race. She starts out her training run by moving at a constant pace of 4.3m/s for 19min. Then she accelerates at a constant rate until she crosses the finish line 19.4s later. What is her acceleration during the last portion of the training run?

Free Fall - the motion of an object due to the force of gravity (air resistance = 0).

• Neglecting air resistance, all objects in free fall have the same acceleration.

• Earth: g (acceleration due to gravity) = 9.8m/s2

• Sun: g = 275m/s2

• Venus: g = 8.9m/s2

• Moon: g = 1.6m/s2

• Jupiter: = 25m/s2

http://imagecache2.allposters.com/images/pic/EUR/2300-2025~Skydiving-Free-Fall-Formation-Posters.jpg

http://www.robhainey.com/Made%20up%20signs/Constuction%20site/Warning%20falling%20objects%20400%20x%20300.jpg

This same acceleration constant (9.8m/s2) applies to objects falling towards earth or moving away from earth.

http://www.onlinephys.com/freefall1.jpg

•When solving for free fall these same equations apply:

vf = vi + atf

df = di + vitf + 1/2at2

vf2 = vi

2 + 2a(df - di)

http://ww1.prweb.com/prfiles/2006/10/04/0000446911/spudwebb.jpg

Examples

• You toss a ball up in the air at 35m/s. What is the velocity of the ball after 2.2s? 4.4s? 7.0s?

• A construction worker accidentally drops a brick for a high scaffold. What is the velocity of the brick after 4.0s? How high was the scaffold?

• A tennis ball is thrown straight up with an initial speed of 22.5m/s. How high does the ball rise? If the ball is caught at the same distance above the ground how long was the ball in the air?

• The current world record for vertical leap is 1.5m. What was this individual’s initial speed? During this jump how long was the person in the air?