1. Speed and Velocity Speed and Velocity
What is speed, velocity and acceleration?
Speed and Velocity
(Use with Speed, Velocity and Acceleration handout)

2. Distance: meters (m), miles (mi)
Speed is the distance traveled per unit of time.
Speed (s) =
distance (d)
time (t)
Each variable measured by units:
Distance: meters (m), miles (mi)
Time:seconds (s), hours (hr), minutes (min)
Speed: meters per second (m/s),
miles per hour (mi/hr),
kilometers per hour (km/hr)

3. Instantaneous, Average, Constant
3 TYPES OF SPEED
Instantaneous, Average, Constant
Pretend you are looking at your car's speedometer while you are driving. The reading you get from your speedometer is
A. instantaneous speed…
This is the speed that you are traveling at that moment.

4. B. Constant Speed is when the object covers equal distances in equal amounts of time.
C. Average speed is the total distance traveled divided by the total time. It can be calculated using the following formula:
speed =
distance
time
Average Speed is:
Total distance = all distance traveled
over
Total time =
final time (end) minus initial time (beginning)
...or shortened:

5. Four Step Approach to Solving Problems G.U.E.S.S.A.
Step 1 READ THE PROBLEM. Draw a picture.
Step 2 IDENTIFY THE VARIABLES
Write down what you know. GIVEN What are you trying to find? UNKNOWN
Step 3 WRITE FORMULA EQUATION
Set up the formula. (The formula should match the unknown.)
Step 4 PLUG IN THE NUMBERS SUBSTITUTE
DO THE MATH SOLVE.
Check ANSWER with UNITS

6. “A car traveled 110 miles in 2 hours.”
Consider the problem…
“A car traveled 110 miles in 2 hours.”
Step 1 Read the problem. Draw a picture.
110 miles
2 hours
Formula
Plug-in
Answer
d =
t =
s =
Units, units, units!

7. ? “A car traveled 110 miles in 2 hours.” 110 miles 2 hours Formula
Step 2 Write down what you know. GIVEN What are you trying to find? UNKNOWN
110 miles
2 hours
Formula
Plug-in
Answer
d =
110 miles
t =
2 hours
s = ?
Units, units, units!

8. FORMULA SHOULD MATCH THE UNKNOWN
“A car traveled 110 miles in 2 hours.”
Step 3 Set up the formula.
FORMULA SHOULD MATCH THE UNKNOWN
s = d t
Formula
Plug-in
Answer
d =
110 miles
t =
2 hours
s = ?
Units, units, units!

9. ? “A car traveled 110 miles in 2 hours.” Formula Plug-in Answer d =
Step 3 Set up the formula. EQUATION
Formula
Plug-in
Answer
d =
110 miles
t =
2 hours d
S =
s = ? t
Units, units, units!

10. “A car traveled 110 miles in 2 hours.”
Step 4 Plug-in the numbers. SUBSTITUTE AND SOLVE. CHECK UNITS 55
mi/hr
Formula
Plug-in
Answer
d =
110 mi
2 hours
t = d
110 mi
S =
S =
S = 55
mi/hr
s = 55
mi/hr t
2 hr
Units, units, units!

11. Do the problems 1-3 on your notes.

12. CIRCLE AND LABEL INFO PROVIDED!
Consider the problem…
“A runner’s average speed during the 10 kilometer race was 20 km/hr. What was his time?’”
Step 1 Read the problem. Draw a picture.
CIRCLE AND LABEL INFO PROVIDED!
Speed of runner: 20 km/hr
10 km
Formula
Plug-in
Answer
d =
t =
s =
Units, units, units!

13. “A runner’s average speed during the 10 kilometer race was 20 km/hr
“A runner’s average speed during the 10 kilometer race was 20 km/hr. What was his time?”
Step 2 Write down what you know. GIVEN What are you trying to find? UNKNOWN
Speed of runner: 20 km/hr
10 km
Formula
Plug-in
Answer
d =
10 km
t = ?
s =
20 km/hr
Units, units, units!

14. “A runner’s average speed during the 10 kilometer race was 20 km/hr
“A runner’s average speed during the 10 kilometer race was 20 km/hr. What was his time?’”
Step 3 Set up the formula. FORMULA MUST MATCH UNKNOWN
t = d s
Formula
Plug-in
Answer
d =
10 km
t (hr) =
d (km)
s (km/hr)
t = ?
s =
20 km/hr
Units, units, units!

15. “A runner’s average speed during the 10 kilometer race was 20 km/hr
“A runner’s average speed during the 10 kilometer race was 20 km/hr. What was his time?’”
Step 4 SUBSTITUTE AND SOLVE
Plug-in the numbers and do the math.
Check units for answer.
Time: 0.5 Hour
Formula
Plug-in
Answer
d =
10 km
0.5 hr
t = d s
10 km
1 r
t =
t (hr)
10 km = =
0.5 hr
20 km/hr
20 km/hr
s =
20 km/hr
Units, units, units!

16. Do the problems 4-5 on your notes.

17. “You decide to go to Dallas to see friends
“You decide to go to Dallas to see friends. Your friends tell you that it takes 4 hours to get to Dallas at an average speed of 70 miles per hour. Approximately how many miles is it to their house?”
70 miles per hour
Step 1 Read the problem. Draw a picture.
Step 2 Write down what you know. GIVEN What are you trying to find? UNKNOWN ?
Step 3 Set up the formula. EQUATION
Step 4 Plug-in the numbers. SUBSTITUTE Do the math. SOLVE. ANSWER with correct unit.
Formula
Plug-in
Answer
d =
280 mi
4 hr
t =
d = s * t
d =70 mi/hr * 4 hr =
280 mi
s =
70 mi/hr
Units, units, units!

18. Do problem 6 on your notes.

19. Instantaneous speed (Reading on your speedometer)
and Average speed (Total distance traveled over total time)
Both do not involve direction.

20. What is the difference between speed and velocity?
55 mi/hr
Velocity has speed & direction.
55 mi/hr
All of these cars had different velocities because they were traveling in different directions.
55 mi/hr

21. A distance/time graph makes it possible to “see” speed.
This graph shows how fast the swimmers went during their workout.
This graph shows how fast the swimmers went during their workout.
Which swimmer swam at a constant (the same) speed throughout her workout?
Constant speed
Is a straight line
Which one stopped during his/her workout?
Stopped here
400 meters at 10, 15, & 20 minutes

22. Make the speed graph
& answer the questions.

23. Acceleration

24. Acceleration is defined as the change in velocity over time.
Any time an object's velocity is changing, we say that the object is accelerating.
This brings up an important point. In common language, when things speed up, we say that they are "accelerating," and, when they slow down, we say that they are "decelerating."

25. However, in the language of physics, we say that both objects are accelerating, not because both objects are speeding up, but because both objects have changing velocities.
POSITIVE ACCELERATION (SPEEDING UP)
* NEGATIVE ACCELERATION (DECELERATING) SLOW DOWN

26. Acceleration is defined as the change in velocity over time.
final velocity – initial velocity
time
acceleration =
Vf - Vi t
a =

27. A go-cart started from the top of a hill at 5 meters per second
A go-cart started from the top of a hill at 5 meters per second. At the bottom of the hill it ended up with a speed of 35 meters per second 6 seconds later. What was the acceleration of the go-cart?
Step 1 Read the problem. Draw a picture.
5 m/s
top
Vf =
In 6 s
Formula
Plug-in
Answer
Vi=
t =
a =
bottom
35 m/s

28. A go-cart started from the top of a hill at 5 meters per second
A go-cart started from the top of a hill at 5 meters per second. At the bottom of the hill it ended up with a speed of 35 meters per second 6 seconds later. What was the acceleration of the go-cart?
Start:
initial Velocity
Step 2 Write down what you know. What are you trying to find?
5 m/s
top
final velocity – initial velocity
acceleration =
time
Vf =
35 m/s
6 s
Formula
Plug-in
Answer
Vi=
5 m/s
t =
6 s
a = ?
bottom
Finish:
final Velocity
35 m/s

29. A go-cart started from the top of a hill at 5 meters per second
A go-cart started from the top of a hill at 5 meters per second. At the bottom of the hill it ended up with a speed of 35 meters per second 6 seconds later. What was the acceleration of the go-cart?
Initial Velocity
Step 3 Set up the formula.
5 m/s
top
Vf - Vi t
Vf =
35 m/s
Formula
Plug-in
Answer
6 s
Vi=
5 m/s
Vf - Vi t
t =
6 s
a = ?
bottom
35 m/s
Final Velocity

30. Step 4 Plug-in the numbers. Solve.
A go-cart started from the top of a hill at 5 meters per second. At the bottom of the hill it ended up with a speed of 35 meters per second 6 seconds later. What was the acceleration of the go-cart?
Step 4 Plug-in the numbers. Solve.
Vf =
35 m/s
Formula
Plug-in
Answer
Vi=
5 m/s
Vf - Vi
35m/s – 5 m/s
30 m/s =
5 m/s2
t =
6 s t 6s
6 s
a =
5 m/s2

31. 5 m/sec2 5 m/sec increase in speed every second. 0 sec 0 m/sec

32. Do the problems 8-9 on your notes.

33. 70 mi/h 70 mi/h 70 mi/h 70 mi/h 70 mi/h 70 mi/h
Velocity involves both speed and direction. Changing velocity does not have to necessarily involve a change in speed. It could just involve a change in direction.
70 mi/h
70 mi/h
70 mi/h

34. Think Differently About Acceleration
1. Consider a car moving at a constant speed of 55 mph while turning in a circle.
Constant Speed of 55 mph
2. The car's velocity is not constant, even though the speed is constant.
3. WHY? This is because the direction of motion is constantly changing while the car is turning around the track.
4. Since the direction is changing, even though the speed is not, the velocity is changing (velocity involves both speed and direction).

35. Think Differently About Acceleration
Constant Speed of 55 mph
5. The car is accelerating because its velocity is changing.
6. As a result, the car is accelerating, even though it is neither speeding up nor slowing down.

36. Speed of Sound
If you shout at a wall that is 40 meters away how long will it take before you hear the echo of your voice. (The speed of sound = 343 m/sec)

37. Speed of Sound
If you shout at a wall that is 40 meters away how long will it take before you hear the echo of your voice. (The speed of sound = 343 m/sec)
V = D = T = 80
T T
T = .23 seconds

38. Speed of Sound
A lightening bolt flashes in the distance and 5 seconds later you hear the clash of thunder. How far away was the lightening? (Speed of sounds = 343 m/sec)

39. Speed of Sound
A lightening bolt flashes in the distance and 5 seconds later you hear the clash of thunder. How far away was the lightening? (Speed of sounds = 343 m/sec)
V = D = D D = 1715 m T

40. Speed of Light
Light from the sun is traveling at a speed of 186,000 miles/sec. It takes light 8 minutes to reach the Earth. Calculate the distance from the Earth to the sun.

41. Speed of Light
Light from the sun is traveling at a speed of 186,000 miles/sec. It takes light 8 minutes to reach the Earth. Calculate the distance from the Earth to the sun.
V = D ,000 = D T
D = 89,280,000 miles