1. One last thing about motion graphs

2. Velocity vs. time graphs (v vs. t)
The total area under the line tells you the change in displacement (change in position) for the object in motion.
What is the change of displacement of the object from t=0s to t=8s?
160 m

3. Velocity vs. time graphs (v vs. t)
Areas can be negative as well. In the case draw the line to the zero x axis.
What is the change of displacement of the object from t=14s to t=20s?
-8 m

4. Symbols and SI Units Displacement (x, xo); meters (m)
Velocity (vf, vo); meters per second (m/s)
Acceleration (a); meters per s2 (m/s2)
Time (t); seconds (s)

5. Constant Acceleration
Setting to = 0 and solving for v, we have:
Final velocity = initial velocity + change in velocity

6. Formulas based on definitions:
Derived formulas:
For constant acceleration only

7. Use of Initial Position x0 in Problems.
If you choose the origin of your x,y axes at the point of the initial position, you can set x0 = 0, simplifying these equations.
The xo term is very useful for studying problems involving motion of two bodies.

8. Problem Solving Strategy:
Draw and label sketch of problem.
Indicate + direction and force direction.
List givens and state what is to be found.
Given: ____, _____, _____ (x,v,vo,a,t)
Find: ____, _____
Select equation containing one and not the other of the unknown quantities, and solve for the unknown.

9. Step 2. Indicate + direction and F direction.
Example 1: A airplane flying initially at 400 m/s lands on a carrier deck and stops in a distance of 300 m. What is the acceleration?
300 m
+400 m/s vo
v = 0 F
X0 = 0 +
Step 1. Draw and label sketch.
Step 2. Indicate + direction and F direction.

10. Example: (Cont.) 300 m +400 m/s vo v = 0 + F
Step 3. List given; find information with signs.
Given: vo = +400 m/s
v = 0
x = +300 m
List t = ?, even though time was not asked for.
Find: a = ?; t = ?

11. Step 4. Select equation that contains a and not t.
Continued . . .
300 ft
+400 ft/s vo
v = 0 + F x
X0 = 0
Step 4. Select equation that contains a and not t.
2a(x -xo) = v2 - vo2
Initial position and final velocity are zero.
a = =
-vo2 2x
-(400 m/s)2
2(300 m)
a = m/s2
Why is the acceleration negative?
Because Force is in a negative direction!

12. CONCLUSION OF Acceleration