1. Uniformly Accelerated Motion
Chapter 2
Uniformly Accelerated Motion

2. Speed

3. Velocity

4. Acceleration
What are the units for acceleration?

5. Uniformly Accelerated Motion Along a Straight Line
In this case…
acceleration is a constant
and the acceleration vector lies in the line of the displacement vector.

6. The 5 Equations!
(1)
(2)
(3)
(4)
(5)

7. Problem Solution Guidelines
Draw a sketch
Indicate origin and positive direction
List the given quantities using the symbols of the equations. (si, vi, a)
Is time known or do we need to find it?
What are we to solve for?
Write the general equations of kinematics

8. More Guidelines
Rewrite the general equations using the known quantities.
Look at the knowns and unknowns and map a strategy of solution.
Check your units
Make sure you are answering the question.

9. Problem Solution Time
Fifteen minutes

10. Definitions Instantaneous Velocity Instantaneous Acceleration
the slope of the displacement versus time graph
Instantaneous Acceleration
the slope of the velocity versus time graph

11. Slopes
Displacement A B
Time

12. Teaming Exercise
Next Problem solutions

13. Free Fall The force of gravity points downward Air resistance ignored
Acceleration of gravity near the surface of Earth is called g = 9.8 m/s2 = 32.1 ft/s2
Air resistance ignored
We have then the conditions of one-dimensional kinematics – straight line motion with constant acceleration.

14. Sample Problem
A ball is thrown vertically upward at 10 m/s. How high will it get, how long will it be in the air, and how fast will it be moving when it hits the ground.

15. Projectile Problems – Two Dimensional Kinematics
Ignore air resistance.
ax = 0
ay = g = 9.81 m/s2 downward

16. The motions in the two directions are independent
Horizontal
Vertical

17. Real Motion is the Combination of the Two

18. 2-D Problem Guidelines Set up two 1-D solutions Origin x Origin y
Positive x Positive y
xi = yi =
vxi = vyi =
ax = 0 ay = g

19. 2-D Guidelines Cont’d
Write general kinematic equations for each direction
Rewrite them for the problem at hand
Find the condition that couples the motions (usually time)

20. Uniformly Accelerated Motion Along a Straight Line