science

1. Distance, Displacement,
Speed, Velocity

2. Motion
►Motion – an object’s change in position
relative to a reference point

3. Reference Point
►The Earth’s surface is used as a common
reference point
►A moving object can be used as a
reference point as well

4. Distance
 Distance (d) – how far an object travels.
 Does not depend on direction.
 Imagine an ant crawling along a ruler.
 What distance did the ant travel?
 d = 3 cm
cm
0 1 2 3 4 5 6 7 8 9 10

5. Distance
 Distance does not depend on direction.
 Here’s our intrepid ant explorer again.
 Now what distance did the ant travel?
 d = 3 cm
 Does his direction change the answer?
cm
0 1 2 3 4 5 6 7 8 9 10

6. Distance
 Distance does not depend on direction.
 Let’s follow the ant again.
 What distance did the ant walk this time?
 d = 7 cm
cm
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7. Example:
 Stan walks 10 km to the grocery store. He
shops then walks back 10 km back to his
house. What distance did he cover?

8.  Tyler drives 50km. Tyler then drives back
30km. What distance did he cover?

9. Displacement
 Displacement (d) – difference between an object’s
final position and its starting position.
 Does depend on direction.
 Displacement = final position – initial position
 d = dfinal – dinitial
 In order to define displacement, we need directions.
 Examples of directions:
 + and –
 N, S, E, W
 Angles

10. Displacement vs. Distance
 Example of distance:
 The ant walked 3 cm.
 Example of displacement:
 The ant walked 3 cm EAST.
 An object’s distance traveled and its
displacement aren’t always the same!

11. cm
0 1 2 3 4 5 6 7 8 9 10
+
-
Displacement
 Let’s revisit our ant, and this time we’ll find
his displacement.
 Distance: 3 cm
 Displacement: +3 cm
 The positive gives the ant a direction!

12. Displacement
 Find the distance and displacement of the
ant.
 Distance: 7 cm
 Displacement: +3 cm
cm
0 1 2 3 4 5 6 7 8 9 10
+
-

13. Example:
 Stan walks 10 km west to the grocery
store. He shops then walks back 10 km
east back to his house. What distance did
he cover? What was his displacement?

14.  Tyler drives 50km north. Tyler then drives
back 30km south. What distance did he
cover? What was his displacement?

15. 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

16. Speed
 Speed (s) – Rate at which an object is
moving.
 speed = distance / time
 s = d/t
 Like distance, speed does not depend on
direction.

17. Speed
 A car drives 100 meters in 5 seconds.
 What is the car’s average speed?
 s = d/t
 s = (100 m) / (5 s) = 20 m/s
100 m
1 s
2 s
3 s
4 s
5 s

18. Speed
 A rocket is traveling at 10 m/s. How long does it
take the rocket to travel 30 m?

19. Speed
 A racecar is traveling at 85.0 m/s. How far
does the car travel in 30.0 s?

20. EXAMPLE:
 If a car travels 400m in 20 seconds how
fast it going?

21.  You arrive in my class 45 seconds after
leaving math which is 90 meters away.
How fast did you travel?

22.  How much time will it take for a bug to
travel 5 meters across the floor if it is
travelling at 1 m/s?

23. Velocity
 Velocity (v) – speed with direction.
 velocity = displacement / time
 v = d / t
 Has magnitude and direction!
 Magnitude – a measure that has a value

24. Pulling It All Together
 Back to our ant explorer!
 Distance traveled: 7 cm
 Displacement: +3 cm
 Average speed: (7 cm) / (5 s) = 1.4 cm/s
 Average velocity: (+3 cm) / (5 s) = +0.6 cm/s
cm
0 1 2 3 4 5 6 7 8 9 10
+
-
1 s
2 s
3 s
4 s
5 s

25. Example:
 A vehicle travels 2345 m west in 315
seconds toward the evening sun. What is
the average velocity?

26. A caterpillar travels across the length of
a 2.00 m porch in 6.5 minutes. What is
the average velocity of the caterpillar in
m/s?

27. A trucker drives along a straight
highway for 0.25 h with a displacement
of 16 km south. What is the trucker’s
average velocity?

28. ACTIVITY:
1. What distance will a car travelling 65
km/hr, cover in 3.0 hrs?
2. A car drives 12 m/s South for 5.0
seconds, then 18 m/s North for 9.0
seconds and finally 15 m/s South for 11
seconds. Calculate the average speed
and average velocity.

29. 3. A car moved 20 km East and 70 km west.
What is the distance?
4. A car moved 50 km North and 25 km
South. What is its displacement?

30. A man walks 7 km in 2 hours and 2 km in 1
hour in the same direction.
a) What is the man's average speed for the
whole journey?
b) What is the man's average velocity for the
whole journey?

31. 5. How far will a car travel in 15 mins at 20
m/s?
6. A rabbit and a turtle are practicing for their
big race. The rabbit covers a 30 m practice
course in 5 seconds, the turtle covers the
same distance in 120 seconds. If the actual
race on 96 m course, by how many seconds
will the rabbit beat the turtle?

32. Bill and Amy want to ride their bikes from
their neighborhood to school which is 14.4
kilometers away. It takes Amy 40 minutes to
arrive at school. Bill arrives 20 minutes after
Amy. How much faster (in meters/second) is
Amy’s average speed for the entire trip?

33. 7. A car moved 60 km East and 90 km west.
What is the displacement?
8. What is the average velocity of a car that
moved 60km East in 3 hours?

34. A car drives 12 m South for 5.0 seconds
then 18 m for 9.0 seconds.
A. Calculate the average speed
B. Calculate the average velocity

35. 9. Joey drives his Skiddo 7 km North. He
stops for lunch and then drives 5 km east.
What distance did he cover? What was his
displacement?
10. You need to get to class, 200 m away
and you can only walk in the hallways at
about 1.5 m/s. How much time will it take to
get to your class?

36. ACCELERATION

37. What does acceleration
mean?
 Compared to displacement and velocity,
acceleration is like the angry, fire-breathing
dragon of motion variables. It can be violent;
some people are scared of it; and if it's big, it
forces you to take notice. That feeling you get
when you're sitting in a plane during take-off,
or slamming on the brakes in a car, or turning a
corner at a high speed in a go kart are all
situations where you are accelerating.

38. Acceleration
the name we give to any process
where the velocity changes. Since
velocity is a speed and a direction,
there are only two ways for you to
accelerate: change your speed or
change your direction—or change
both.

40. If you’re not changing your speed and
you’re not changing your direction, then
you simply cannot be accelerating—no
matter how fast you’re going. So, a jet
moving with a constant velocity at 800
miles per hour along a straight line has
zero acceleration, even though the jet is
moving really fast, since the velocity
isn’t changing. When the jet lands and
quickly comes to a stop, it will have
acceleration since it’s slowing down.

41. Or, you can think about it this way. In a
car you could accelerate by hitting the
gas or the brakes, either of which would
cause a change in speed. But you could
also use the steering wheel to turn,
which would change your direction of
motion. Any of these would be
considered an acceleration since they
change velocity.

42. What's the formula for acceleration?
To be specific, acceleration is defined to
be the rate of change of the velocity.

43. The acceleration formula can be
rearranged to solve for other variables
such as final speed (v2) and time (t).

44. EXAMPLE
A neurotic tiger shark starts from rest
and speeds up uniformly to 12 meters
per second in a time of 3 seconds.
What was the magnitude of the
average acceleration of the tiger
shark?

46. A race car starts from rest and
speeds up uniformly to the right
until it reaches a maximum velocity
of 60 m/s in 15 s. What is the
acceleration of the race car?

47. A car accelerates uniformly from
22.5 m/s to 46.1 m/s in 2.47
seconds. Determine the
acceleration of the car.

48. A parachute on a racing
dragster opens and changes the
speed of the car from 85 m/s to
45 m/s in a period of 4.5
seconds. What is the
acceleration of the dragster?

49. A motorcycle traveling at 25
m/s accelerates at a rate of 7.0
m/s2 for 6.0 seconds. What is
the final speed of the
motorcycle?

50. A cyclist accelerates at a rate of 7.0
m/s2. How long will it take the
cyclist to reach a speed of 18 m/s?