SPEED AND
ACCELERATION
 Motion-a change in position.
 Position- where an object is at a specific time
(including direction)
 Ex. 7km North of Building A
 Distance-interval of length – doesn’t include
direction
 Ex. I walked 14km
 An object at rest is a special case of motion in
which there is not change in position
Speed vs. Velocity
 Speed-the distance an object travels over a
certain amount of time
 Speed is the rate of motion without direction
 Rate-ratio between two different quantities
(distance/time)
 Units: m/s or km/hr
 Formula:
Speed =d/t (speed=distance/time)
 Constant speed-the speed does not change
 Instantaneous speed- the speed at a single
instant/moment of time
Speed vs. Velocity
 Velocity – change in position an object travels
over a certain amount of time
 Velocity includes a component of direction
 Units: Same as speed
 Formula:
𝑐ℎ𝑎𝑛𝑔𝑒 𝑖𝑛 𝑝𝑜𝑠𝑖𝑡𝑖𝑜𝑛
V=
𝑐ℎ𝑎𝑛𝑔𝑒 𝑖𝑛 𝑡𝑖𝑚𝑒
 Direction can be shown by positive or negative
signs.
 Moving “forward” is positive
 Moving “backward” is negative
 Direction can be shown by using compass directions
 Moving 35 mph north.
Position Graph
Position vs. Time
160
Position (miles)
140
120
100
80
60
40
20
0
1
2
3
Time (hours)
4
5
How does graphing fit in?
(It’s never going to go away!)
 Position vs. Time graphs show where things
are at different times which makes it easy to
see how things have moved.
 EX:
P
P
T
Moving Away
(forward)
P
T
T
Moving to Start Stopped
(backward)
(no motion)
Changing Motion
 How can the motion of an object be changed?
 Change how fast it is moving
 Speed Up
 Slow Down
 Change direction
*Note: Changing direction changes
the velocity but not the speed.
Keep the graphing coming!!!
 Distance vs. Time Graphs - show how long it
takes an object to travel over a certain distance
 Show the motion of objects over a period of time
 Slope shows how speed changes at different places
D
D
T
Increasing
D
T
Decreasing
T
Constant
 Acceleration- the rate at which velocity
changes
 Formula:
𝑐ℎ𝑎𝑛𝑔𝑒 𝑖𝑛 𝑣𝑒𝑙𝑜𝑐𝑖𝑡𝑦
a=
𝑐ℎ𝑎𝑛𝑔𝑒 𝑖𝑛 𝑡𝑖𝑚𝑒
 Example of units on acceleration:
 m/s2 or m/s/s
Velocity Graph
Velocity vs. Time
6
Velocity (m/s)
5
4
3
2
1
0
1
2
3
4
Time (seconds)
5
6
Even more Graphing…….awwww yeah!!!
• Velocity vs. Time Graphs- show how fast an
object is traveling at a specific moment of time
—Slope shows how an object is accelerating
V
V
T
V
T
Positive
Negative
Acceleration
Acceleration
T
No Acceleration
(constant velocity)
Discussion
 In a position vs. time graph, what does a
negative slope mean?
 In a velocity vs. time graph, what does a
negative slope mean?