RELATING SPEED TO DISTANCE AND TIME

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RELATING SPEED TO DISTANCE AND TIME

• Chapter 9.5

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3 TYPES OF SPEED

• 1) AVERAGE SPEED
• Is the total distance divided by the total time
  for an entire trip.
• Think starting and stopping (bathroom breaks)
• 2) INSTANTANEOUS SPEED
• Is the speed of an object at any instant in time.
  
• Think radar gun
• 3) CONSTANT SPEED
• Is when an object remains at the same
  instantaneous speed over a period of time
• Think cruise control

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• Speed (velocity) is a measure of the time
  required for an object to travel a certain
  distance.
• Often measured in m/s or km/h
• Distance is the amount of space between two
  points or objects.
• Units used for distance is cm, m, km
• Time is the duration between two events
• Units used for time are s, min, hr
• Note We need to measure distance and time in
  order to determine the speed of an object.

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• Formula for speed (or velocity)
• V d (distance)
• t (time)
• Formula for average speed
• Vav ? d (d2 d1 )
• ? t (t2 - t1)
• (delta - ?) Greek Symbol meaning a change in
• d2 is final distance t2 is final time
• d1 is initial distance t1 is the initial time

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FORMULA FOR SPEED

• V d2 d1
• t2 t1
• v speed (velocity) measured in m/s or km/h
• d change in distance measured in mm, cm, m,
  km
• t change in time measured in sec, min, hour,
  year(a)

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EXAMPLES

• 1) Eiko skates to school, a total distance of 4.5
  km. She has to slow down twice to cross busy
  streets, but her overall journey takes 0.62
  hours. What is Eikos average speed during the
  trip?
• Solution

?d 4.5 km , ? t 0.62 h, vav ? vav ? d
4.5 km 7.3 km / h ? t 0.62
h Eikos average skating speed is 7.3 km/h.
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• Imagine that you are riding on the Cariboo
  Dayliner train and you see a sign that reads 120
  km. After seeing several signs like this, you
  decide to time between two of the signs which are
  10 km apart. The elapsed time is recorded at
  390.6 s. What is the speed of the train in km/h?
• SOLUTION

d 10 km , t 390.6 s, v ? t 390.6 s
0.1085 h v d 10 km
92 km/h 3600 s
t 0.1085 h The train is
traveling at 92 km/h.
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• 3) Same information of 2 but the question asked
  for m/s instead of km/h.
• SOLUTION

d 10 km, t 390.6 s , v ? d 10 km x 1000 m
10 000 m v d 10000 m 25.60
m/s 1 km
t 390.6 s The train
is traveling at 25.60 m/s.
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• 4) Kira is trying to predict the time required to
  ride her bike to the nearby beach. She knows
  that the distance is 45 km and from other trips,
  she can average about 20 km/h. How long will her
  trip take?
• SOLUTION

? d 45 km, vav 20 km/h, ? t ? Rearrange
Formula for t. ? t ? d 45 km 2.3 h
vav 20 km/h Kira should be able t
make the trip in 2.3 h.
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PRACTICE

• Do the 9.5 Supplemental practice problems or 10
  Questions Handout
• Text page 358
• Questions 3,4,8,9,10a, 11ab
• Handout 9.5b , 9.5 d