Speed and Acceleration
Measuring motion
Measuring Distance

Meter – international unit for
measuring distance.
1 mm
= 50 m
Measuring Time

Seconds– international unit for
measuring time.
Calculating Speed

Speed (S) = distance traveled (d) /
the amount of time it took (t).
S=d
t
S
d
t
Units for speed

Depends, but will always be a
distance unit / a time unit
Examples:
 Cars: mi/h
 Jets: km/h
 Snails: cm/s
 Falling objects: m/s
S=d
Calculating speed
t




If I travel 100 kilometer in one hour
then I have a speed of…
100 km/h
If I travel 2 meter in 1 second then I
have a speed of….
2 m/s
Average speed
Average speed = total distance traveled
total time it took.

Speed is usually NOT CONSTANT
Example:
 Cars stop and go regularly
 Runners go slower uphill than downhill
Calculating Average Speed


It took me 1 hour to go 40 km on the
highway. Then it took me 2 more hours to go
20 km using the streets.
Total Distance:


Total Time:


40 km + 20 km = 60 km
1 h + 2 h = 3 hr
Ave. Speed:

total d/total t = 60 km/3 h = 20 km/h
Total _ Dist .
Ave. _ Speed 
Total _ time
Question

I travelled 25 km in 10 minutes.
How fast did I travel?
Question

I ran 1000 m in 3 minutes. Then
ran another 1000 m uphill in 7
minutes. What is my average
speed?
Total Dist. = 1000 m + 1000 m = 2000 m
Total Time = 3 min + 7 min = 10 min
Ave speed = total dist/total time =
2000m/10 min = 200 m/min = D
Velocity

Velocity – the SPEED and
DIRECTION of an object.

Example:
An airplane moving North at 500 mph
 A missile moving towards you at 200 m/s

Question

What is the difference between
speed and velocity?
 Speed
is just
distance/time. Velocity
includes direction as well.
LET’S PRACTICE!
LET’S REVIEW!
D
Speed
Speed = distance (in meters)
time (in seconds)
S
T
1) Dave walks 200 metres in 40 seconds. What is his speed?
2) Laura covers 2km in 1,000 seconds. What is her speed?
3) How long would it take to run 100 metres if you run at
10m/s?
4) Steve travels at 50m/s for 20s. How far does he go?
5) Susan drives her car at 85mph (about 40m/s). How long
does it take her to drive 20km?
Graphing Speed Worksheet
WHAT THE SLOPE?!?



On a graph, the slope of a line is
found by RISE (Y) over RUN (X).
On a speed graph, distance is on the
Y-axis and time if on the X-axis.
On a speed graph, the slope equals
the speed.
Graphing Speed:
Distance vs. Time Graphs
Denver
Phoenix
Graphing Speed:
Distance vs. Time Graphs
Speed = Slope = Rise/
Rise
Graphing Speed:
Distance vs. Time Graphs
Speed = Slope = Rise/
Rise=?
600 km
3h
Graphing Speed:
Distance vs. Time Graphs
Speed = Slope = Rise/
Rise=?
600 m
3 minutes
Rise/
Distance (km)
Different Slopes
8
7
6
5
4
3
2
1
0
Slope = Rise/Run
= 1 km/1 hr
= 1 km/hr
Slope = Rise/Run
= 0 km/1 hr
= 0 km/hr
Rise = 2 km
Rise = 0 km
Run = 1 hr
Run = 1 hr
Slope = Rise/Run
= 2 km/1 hr
= 2 km/hr
Rise = 1 km
Run = 1 hr
1
2
3
4
Time (hr)
5
6
7
Question
Below=isTotal
a distance
vs. time
graph
ofkm/6 hr
Average Speed
distance/Total
time
= 12
my position =during
a race. What was
2 km/hr
my AVERAGE speed for the entire race?
14
Distance (km)
12
10
8
Rise = 12 km
6
4
2
0
0
1
2
3
Time
Run
= (hr)
6 hr
4
5
6
Question


What does the slope of a distance
vs. time graph show you about the
motion of an object?
It tells you the SPEED
Question

Below is a distance vs. time graph for 3
runners. Who is the fastest?
7
Distance (mi.)
6
5
Bob
Jane
Leroy
4
3
2
1
0
0
1
2
3
4
5
6
35
Time (h)
Leroy is the fastest. He completed the race in 3 hours
Distance-time graphs
40
2) Horizontal line =
4) Diagonal line
downwards =
30
20
Distance(m)
10
0
Time/s
20
1) Diagonal line =
40
Time (s)
60
80
100
3) Steeper diagonal line =
Acceleration



Acceleration = speeding up
Deceleration = Slowing down
Acceleration – the rate at which
velocity changes

Can be an:
Increase in speed
 Decrease in speed
 Change in direction

Types of acceleration

Increasing speed


Decreasing speed


Example: Car speeds up at green light
screeeeech
Example: Car slows down at stop light
Changing Direction

Example: Car takes turn (can be at
constant speed)
Question


How can a car be accelerating if its
speed is a constant 65 km/h?
If it is changing directions it is
accelerating

Ex: Nascar!
Calculating Acceleration

If an object is moving in a straight line
Final _ speed  Initial _ Speed
Acceleration 
Time

Units of acceleration:

m/s2
Calculating Acceleration
Final _ Speed  Initial _ Speed
Acceleration 
Time
16m / s  0m / s

4s
 4m / s 2
0s
0 m/s
1s
4 m/s
2s
8 m/s
3s
12 m/s
4s
16 m/s
Question

A skydiver accelerates from 20 m/s to 40
m/s in 2 seconds. What is the skydiver’s
average acceleration?
Final _ speed  Initial _ speed
Accel 
Time
40m / s  20m / s 20m / s


2s
2s
2
 10m / s
Acceleration (m/s2) = change in velocity (m/s)
time taken (s)
Acceleration
Vf - Vi
a
t
1) A cyclist accelerates from 0 to 10m/s in 5 seconds. What is
her acceleration?
2) A ball is dropped and accelerates downwards at a rate of
10m/s2 for 12 seconds. How much will the ball’s velocity
increase by?
3) A car accelerates from 10 to 20m/s with an acceleration of
2m/s2. How long did this take?
4) A rocket accelerates from 1,000m/s to 5,000m/s in 2
seconds. What is its acceleration?
Graphing Acceleration


Velocity vs. Time
Acceleration = slope = rise/run
14
Y-Axis = Speed
Speed (m/s)
12
10
8
6
4
2
0
0
1
2
3
Time (s)
X-Axis = Time
4
5
6
Graphing Acceleration:
Speed vs. Time Graphs
14
Speed (m/s)
12
10
8
6
4
2
0
0
1
2
3
4
5
6
Time (s)
1)Line is straight = acceleration is constant
2)Flat line = constant speed
Graphing Acceleration:
Speed vs. Time Graphs
14
Speed (m/s)
12
10
8
Rise = 4 m/s
6
4
Run = 2 s
2
0
0
1
2
3
4
5
Time (s)
1)In Speed vs. Time graphs:
SLOPE = Acceleration = Rise/Run
= 4 m/s ÷ 2 s = 2 m/s2
6
Question
14
Speed (m/s)
12
10
Run = 3 s
8
6
Rise = -6 m/s
4
2
0
0
1
2
3
4
5
Time (s)
Above is a graph showing the speed of a car over time.
1. How is the speed of the car changing
(speeding up, slowing down, or staying the same)?
2. What is this car’s deceleration?
1) The car is slowing down
2) Deceleration = rise/run = -6m/s ÷3s = -2 m/s2
6
Velocity-time graphs
1) Upwards line =
80
4) Downward line =
60
Velocity 40
m/s
20
0
10
2) Horizontal line =
20
30
40
50
3) Upwards line =
Time (s)
80
Velocity (m/s)
60
40
20
0
Time (s)
10
20
30
40
1) How fast was the object going after 10 seconds?
2) What is the acceleration from 20 to 30 seconds?
3) What was the deceleration from 30 to 50s?
4) How far did the object travel altogether?
50