Kinematics – How things Move
Time
t = tf – ti
Distance
d = df – di
Average Velocity
Velocity
v = vf – vi
Average Acceleration
v = d
t
a = v
t
Speed is the absolute value of velocity.
Speed vs. Velocity
Speed is a scalar – has magnitude
Velocity is a vector – has magnitude and direction
Speed = d
Distance Traveled
Distance
Traveled
Time of Travel
Velocity = Displacement
Time of Travel
Displacement =  position
Acceleration
Example: You travel a distance of 12 meters in 24 seconds along the following path. What is your speed and your velocity?
4 m
2 m
Speed vs. Velocity
Acceleration – A change in velocity over time
This can be a change in speed
Ex. Speeding up or slowing down
This can be a change in direction
Ex. Making a turn, even at constant speed
2 m
4 m
Speed =
12 m
= 0.5 m/s
24 s
Velocity =
0 m
= 0 m/s
24 s
Motion Sign Conventions
+
‐
d
Forward/Up
Backward/Down
v
M
Move Forward
F
d
M
Move Reverse
R
Speeding Up or Slowing Down or a
Slowing Down
In Reverse
Speeding Up
In Reverse
You can “feel” when acceleration happens when a car changes speeds or makes sharp turns
4
Motion Equations
d = vi t + ½ a t2
vf = vi + a t
vf2 = vi2 + 2 a d
+ 2ad
d ‐ displacement
a ‐ acceleration
t ‐ time
vf ‐ final velocity
vi ‐ initial velocity
vi is often written vo
1
2 More Motion Equations
Free Fall
d = vf t ‐ ½ a t2
Falling objects have acceleration due to gravity . • Equations use g for a
• Down is negative
d = ½ (vi + vf) t
From combining the other equations we can remove some variables.
These can be helpful!!
Ex: d = vi t + ½ g t2
g = – 9.8 m/s2
A foul ball is hit straight up into the air with a speed of 25m/s. How high does it go and how long is it in the air?
Use the following table to organize information
Fill in all given information
Use equations to find unknowns one by one
First!! ‐ Draw a picture and determine what two points to use
Point 1 is the maximum height (and half flight time).
vf
1
vf 0 m/s – Assumed
a
vi 25 m/s ‐ Given
d
a
t
d
i
t
Vi = 25 m/s
Use equations to find unknowns
To find max height, use an equation with only d as an unknown
‐9.8 m/s2 ‐ Given
d = vf ‐
2 a
vi2
= (0m/s) 2
vf = vi + a t
(25 m/s)2
‐
2 (‐9.8 m/s2)
= 31.9 m d 31.9 m
t
Vf = 0 m/s
0 m/s
1
vf ‐25 m/s – Assumed
vi 25 m/s ‐ Given
a
vf ‐ vi
‐25 m/s ‐ 25 m/s
= = 5.1 s a
‐9.8 m/s2
Initial to Point 2
Initial to Point 2
1
vf 0 m/s – Assumed
‐9.8 m/s2
t = Vf = 0 m/s
0 m/s
Initial to Point 1
Initial to Point 1
2
Vf = ‐25 m/s
To find total flight time, use an equation with only t as an unknown
Use assumptions from Point 2 for data.
vf2 = vi2 + 2 a d
2
Vf = 0 m/s
0 m/s
Initial to Point 1
Initial to Point 1
vi
vi 25 m/s ‐ Given
‐ Given
a
i
Vi = 25 m/s
2
Vf = ‐25 m/s
‐9.8 m/s2 ‐ Given
d 0 m – Assumed
t
5.1 s
i
Vi = 25 m/s
2
Vf = ‐25 m/s
2