1. Physics Principles and Problems
Accelerated Motion
Chapter 3
Physics Principles and Problems
Zitzewitz, Elliot, Haase, Harper, Herzog, Nelson, Nelson, Schuler and Zorn
McGraw Hill, 2005

2. Acceleration - rate of change in velocity per unit time.
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3. Acceleration = ∆v / ∆t (vf - vi / tf - ti)
8m/s - 4m/s = 4m/s = 2m/s2
4s - 2s s
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?

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

5. The sign of acceleration does not indicate whether or not
Using the graph explain the acceleration and position of these 5 runners (assume east is positive).
east A B v e l o c i t y
(m/s) C D
time (s) E
west
The sign of acceleration does not indicate whether or not
The object is speeding up or slowing down (only its direction).

6. 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?

7. Position with Average Acceleration df = di + vitf + 1/2atf2 Velocity with Constant Acceleration vf2 = 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?

8. 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

9. This same acceleration constant (9
This same acceleration constant (9.8m/s2) applies to objects falling towards earth or moving away from earth.
When solving for free fall these same equations apply:
vf = vi + atf
df = di + vitf + 1/2at2
vf2 = vi2 + 2a(df - di)

10. 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?