Motion, Speed, Velocity, Acceleration

1. Motion
Part 1: Motion and Speed

2. Speed
Speed is the distance an object
travels per unit of time.
To calculate speed:
Speed = Distance ÷ Time
Distance is in meters (m)
Time is in seconds (s)
Speed is in meters per second (m/s)

3. Example 1
A snail takes 5.0 s to crawl across the ruler.
Speed = Distance ÷ Time
Speed = 0.07 m ÷ 5.0 s
Speed = 2.0 m/s

4. Example 2
A car drives 250 m in one minute.
Speed = Distance ÷ Time
Speed = 250 m ÷ 60 s
Speed = 4.17 m/s

5. Use the Formula Triangle!
To calculate
speed:
s t
d
To calculate
time:
To calculate
distance:
s = d / t t = d / s d = s x t

6. Distance vs. Displacement
Distance and displacement are different.
Distance
How far an object
moves in total.
Displacement
The distance and
direction an object
moves from a
starting position.

7. Distance vs. Displacement
Jeffrey, my
distance was
176 meters!
But Billy, your
displacement
was 1 meter!

8. Distance vs. Displacement
90 ft.
Distance = 90 ft. Displacement = 90 ft.

9. Distance vs. Displacement
90 ft.
90 ft.
Distance = 180 ft. Displacement =127 ft.

10. Distance vs. Displacement
90 ft.
90 ft.
90 ft.
Distance = 270 ft. Displacement = 90 ft.

11. Distance vs. Displacement
90 ft.
90 ft.
90 ft.
90 ft.
Distance = 360 ft. Displacement = 0 ft.

12. Any Questions?

13. Motion
Part 2: Distance-Time Graphs

14. Graphing Speed
A distance-time graph shows the motion
of a certain object in line graph form.
The motion of an object can be graphed.
Time is plotted on the horizontal (X) axis
Distance is plotted on the vertical (Y) axis

15. Time (s) Distance (m)
0 0
1 2
2 4
3 6
4 8
5 8
6 8
7 8
8 8
9 12
10 16
Distance-Time Graphs
The slope of a
distance-time
graph is the
speed

16. Distance-Time Graphs
S = D ÷
T
= 8 ÷ 4
= 2 m/s
S = D ÷
T
= 8 ÷ 2
= 4 m/s
S = D ÷ T
= 0 ÷ 4
= 0 m/s

17. Distance-Time Graphs
Constant
speed
(moving away)
Constant
speed
(moving closer)
(and faster!)
No
speed
(standing still)

18. Interpreting a D-T Graph (1)
Time (s)
Distance
(m)
Analysis:
• The distance (m)
stays the same
as the time (s)
increases
• Therefore, the
object is at rest
(not moving)

19. Interpreting a D-T Graph (2)
Time (s)
Distance
(m)
Analysis:
• The object is
moving away
from the
reference point
• The object is
moving at a
constant speed
• The object is
moving quickly

20. Interpreting a D-T Graph (3)
Time (s)
Distance
(m)
Analysis:
• The object is
moving towards
the reference
point
• The object is
moving at a
constant speed
• The object is
moving slowly

21. Interpreting a D-T Graph (4)
Time (s)
Distance
(m)
Analysis:
• In Part A, the
object is moving
away at a
constant speed
• In Part B, the
object is at rest
• In Part C, it is
moving towards
at constant speed
A
B
C

22. Any Questions?

23. Motion
Part 3: Velocity and Acceleration

24. Review: Speed
Speed is the distance an object travels
in a specific amount of time.
To calculate speed:
Speed = Distance ÷ Time
Distance is in meters (m)
Time is in seconds (s)
Speed is in meters per second (m/s)

25. Velocity
For example, sailors must know the speed
and direction their boat is travelling in.
Sometimes, knowing the speed isn’t enough.
Velocity is a description of
both speed and direction.
e.g. a sailboat travelling at
20 kph in a SE direction

26. Velocity
For example, sailors must know the speed
and direction their boat is travelling in.
Sometimes, knowing the speed isn’t enough.
Velocity is an example
of a vector, a quantity
that has both magnitude
and direction.

27. Acceleration
Acceleration measures how much an
object’s speed changes over a certain time.
Objects can speed up, slow down or change direction.
Acceleration can be:
A change in speed
A change in direction
A change in speed & direction

28. Acceleration
Acceleration can be positive, negative or zero.
Negative Acceleration
Positive Acceleration Object speeds up
Object slows down
Zero Acceleration Constant or no speed

29. Acceleration
Formula for acceleration:
acceleration = change in velocity
time
Velocity: meters per seconds (m/s)
Time: seconds (s)
Acceleration: meters per second squared (m/s2)
a = Vfinal - Vinitial
t

30. Example 1
a = Vfinal - Vinitial
t
a = 20.0 m/s - 11.0 m/s
4.0
a = 9.0 m/s
4.0
a = 2.25 m/s2
A motorcycle’s velocity at the top of the hill is
11.0 m/s. 4.0 seconds later it reaches the bottom
of the hill with a velocity of 20.0 m/s. What is the
acceleration of the motorcycle?

31. Example 2
a = Vfinal - Vinitial
t
- 2.9 m/s2 = 0.0 m/s - 13.0 m/s
t
t (- 2.9) = - 13.0 m/s
A speed skater just finished a race. After she crossed
the finish line, she coasted to a complete stop. If her
initial speed was 13.0 m/s and her acceleration was -
2.9 m/s2, how long did it take her to stop?
t = - 13.0 m/s / - 2.9
t = 4.5 s

32. Any Questions?

33. Motion
Part 4: Speed-Time Graphs

34. Interpreting a D-T Graph (1)
Time (s)
Distance
(m)
Analysis:
• The distance (m)
increasing as time
(s) passes
• The distance gets
larger and larger
with each second
• This shows (+)
acceleration

35. Interpreting a D-T Graph (1)
Time (s)
Distance
(m)
Analysis:
• The distance (m)
decreasing as
time (s) passes
• The distance gets
smaller & smaller
with each second
• This shows (-)
acceleration

36. Interpreting a D-T Graph (3)
Time (s)
Distance
(m)
Analysis:
• The distance (m)
from a reference
point is
increasing
• It is increasing at
a regular rate
• This shows (0)
acceleration

37. Interpreting a D-T Graph (3)
Time (s)
Distance
(m)
Analysis:
• The object is
moving towards
the reference
point
• The object is
moving at a
constant speed
• The object is
moving slowly

38. Interpreting a S-T Graph (4)
Time (s)
Speed
(m/s)
Analysis:
• The speed (m/s) is
constant as time
(s) passes
• The object’s
speed is not
changing
• This shows (0)
acceleration

39. Interpreting a S-T Graph (5)
Time (s)
Speed
(m/s)
Analysis:
• The speed (m/s) is
increasing as time
(s) passes
• The object speed
is changing
• This shows (+)
acceleration

40. • A roller coaster is moving at 25 m/s at the
bottom of a hill. Three seconds later it
reaches the top of the hill moving at 10 m/s.
What was the acceleration of the coaster?

41. • A car’s velocity changes from 0 m/s to 30
m/s in 10 seconds. Calculate acceleration

42. • A satellite’s original velocity is 10,000 m/s.
After 60 seconds it s going 5,000 m/s. What
is the acceleration?

43. • If a speeding train hits the brakes and it
takes the train 39 seconds to go from 54.8
m/s to 12 m/s what is the acceleration?

44. Any Questions?