1. 8/30 Describing Motion, Vectors
Text sections and 1.5-6
HW “8/30 Acceleration” due Thur 9/5
On web or in 213 Witmer for copying

2. Imagine a bead on a wire, a ruler, and a timer.
ruler reading
0 0
1 6
2 8
3 6
4 0
5 ?
x = 6
x = 2
x = -2
x = -6
x = ?
vave = 6m/s
vave = 2m/s
vave = -2m/s
vave = -6m/s
vave = ?m/s
t = 1
t = 2
t = 3
t = 4
t = 5
t = 0
v = 4m/s
v = 0m/s
v = -4m/s
v = -8m/s
v = -12m/s
v = 8m/s
What is the instantaneous velocity v when:
-10
-10 m/s
-10
Direction requires a statement about which way is pos. and neg. Must keep track of minus signs
Rather that keeping track of signs, use arrows, let right be positive.

3. Examples of Vectors
An object moving at 16m/s directed 30° above the horizontal
16m/s
30°
The same object moving at 10m/s directed 30° above the horizontal
10m/s
Note that the length corresponds to the magnitude
30°

4. Vectors Quantities with direction Which quantities are vectors?
temperature velocity force volume acceleration mass   
Vectors have two parts, magnitude and direction

5. Question:
A ball rolls up a ramp as shown in the strobe photograph. Which way does the acceleration point or does the acceleration = 0?
Turnaround point
Ball rolling up the ramp v

6. Question:
A ball rolls up and down a ramp as shown in the strobe photograph. At the turnaround point, which way does the acceleration point or does the acceleration = 0 there?
Turnaround point

7. Velocity Vectors Draw velocity vectors for t = 0 - 5
-50
+50
Draw velocity vectors for t = 0 - 5
speeding up from rest and moving right
ruler reading
time
0 0
1 5
2 20
3 45
4 80
5 125
t = 0
v = 0m/s
x = 5
vave = 5m/s
t = 1
v = 10m/s
x = 15
vave = 15m/s
t = 2
v = 20m/s
x = 25
vave = 25m/s
t = 3
v = 30m/s
x = 35
vave = 35m/s
t = 4
v = 40m/s
x = 45
vave = 45m/s
t = 5
v = 50m/s

8. “Change in Velocity” Vector, v
v = 0m/s
v = 10m/s right
v = 10m/s
v = 10m/s right
v = 20m/s
v = 10m/s right
v = 30m/s
v = 40m/s
v = 50m/s

9. Velocity Vectors -5 +5
Slowing down while moving right, turning around, speeding up while moving left
ruler reading
time
0 0
1 6
2 8
3 6
4 0
t = 0
v = 8m/s
x = 6
vave = 6m/s
t = 1
v = 4m/s
x = 2
vave = 2m/s
t = 2
v = 0m/s
x = -2
vave = -2m/s
t = 3
v = -4m/s
x = -6
vave = -6m/s
t = 4
v = -8m/s
x = -10
vave = -10m/s
t = 5
v = -12m/s

10. “Change in Velocity” Vector, v
Even though the object slows down, turns around, and speeds up in the opposite direction; v is constant!
v = 8m/s
v = -4m/s left
v = 4m/s
v = -4m/s left
v = 0m/s
v = -4m/s left
v = -4m/s
v = -4m/s left
v = -8m/s
v = -12m/s
The “change in velocity” vector may point with or against the velocity vector.

11. Acceleration
Acceleration is a vector that points in the same direction as the “change in velocity” vector. In this case, a = 4m/s/s left.
a = v t
In concept, it is “the amount and direction the velocity changes each second.”
v = -4m/s left
v = 8m/s
v = 4m/s
v = 0m/s
v = -4m/s
v = -8m/s
v = -12m/s
v and a point opposite, slowing down
v and a point the same direction, speeding up

12. Question:
A ball rolls up and down a ramp as shown in the strobe photograph. Which way does the acceleration point or does the acceleration = 0? vi
Pick a time interval, ti - tf and draw velocity vectors vf
Draw velocity vectors tail to tail
Draw v, (from i to f) which points the same direction as a.
Turnaround point
Ball rolling up the ramp vi vf v tf ti

13. Question:
A ball rolls up and down a ramp as shown in the strobe photograph. At the turnaround point, which way does the acceleration point or does the acceleration = 0 there?
Turnaround point

14. Problem:
A bear is running 4 m/s north. The acceleration of the bear is 3m/s2 north. What is the bear’s velocity 2 seconds later?
v = 10 m/s north
What is the bear’s average velocity? How far did the bear run during this time?
vave = 7 m/s north
x = 14 m north

15. Problem:
An object goes from a velocity of 15 m/s right to 6 m/s right in 3 seconds. Find the acceleration, both its size (magnitude) and its direction, (left or right).
How do the directions of the velocity and acceleration compare? What is the object doing during these 3 seconds?
How far did the object travel during these three seconds? Hint: What is the average velocity?
What will the objects velocity be in three more seconds if the acceleration stays the same?