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Distance, Displacement, Speed, and Velocity
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
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
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
0 1 2 3 4 5 6 7 8 9 10
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
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!
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!
Displacement
 Find the ant’s displacement again.
 Remember, displacement has direction!
 Distance: 3 cm
 Displacement: -3 cm
cm
0 1 2 3 4 5 6 7 8 9 10
+
-
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
+
-
Displacement vs. Distance
 An athlete runs around a track that is 100 meters
long three times, then stops.
 What is the athlete’s distance and displacement?
 Distance = 300 m
 Displacement = 0 m
 Why?
Speed
 Speed (s) – Rate at which an object is
moving.
 speed = distance / time
 s = d/t
 Like distance, speed does not depend on
direction.
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
Speed
 A rocket is traveling at 10 m/s. How long does it
take the rocket to travel 30 m?
Speed
 A racecar is traveling at 85.0 m/s. How far
does the car travel in 30.0 s?
Velocity
 Velocity (v) – speed with direction.
 velocity = displacement / time
 v = d / t
 Has magnitude and direction!
 Magnitude – a measure that has a value
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

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Distance,_Displacement,_Speed,_and_Velocity_notes.ppt

  • 2. 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
  • 3. 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
  • 4. 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 0 1 2 3 4 5 6 7 8 9 10
  • 5. 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
  • 6. 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!
  • 7. 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!
  • 8. Displacement  Find the ant’s displacement again.  Remember, displacement has direction!  Distance: 3 cm  Displacement: -3 cm cm 0 1 2 3 4 5 6 7 8 9 10 + -
  • 9. 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 + -
  • 10. Displacement vs. Distance  An athlete runs around a track that is 100 meters long three times, then stops.  What is the athlete’s distance and displacement?  Distance = 300 m  Displacement = 0 m  Why?
  • 11. Speed  Speed (s) – Rate at which an object is moving.  speed = distance / time  s = d/t  Like distance, speed does not depend on direction.
  • 12. 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
  • 13. Speed  A rocket is traveling at 10 m/s. How long does it take the rocket to travel 30 m?
  • 14. Speed  A racecar is traveling at 85.0 m/s. How far does the car travel in 30.0 s?
  • 15. Velocity  Velocity (v) – speed with direction.  velocity = displacement / time  v = d / t  Has magnitude and direction!  Magnitude – a measure that has a value
  • 16. 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