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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. Is the total distance divided by the total time for an entire trip. Start to finish. Start to finish. 2) INSTANTANEOUS SPEED Is the speed of an object at any instant in time. Is the speed of an object at any instant in time. Think radar gun Think radar gun 3) CONSTANT SPEED Is when an object remains at the same instantaneous speed over a period of time Is when an object remains at the same instantaneous speed over a period of time Think cruise control Think cruise control

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Speed (velocity) is a measure of the time required for an object to travel a certain distance. 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 Often measured in m/s or km/h Distance is the amount of space between two points or objects. Distance is the amount of space between two points or objects. Units used for distance is cm, m, km Units used for distance is cm, m, km Time is the duration between two events Time is the duration between two events Units used for time are s, min, hr 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.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): Formula for speed (or velocity): V = d (distance) t (time) Formula for average speed: Formula for average speed: V av = Δ d = (d 2 – d 1 ) Δ t (t 2 - t 1 ) Δ t (t 2 - t 1 ) (delta - Δ) – Greek Symbol meaning a change in d 2 is final distancet 2 is final time d 1 is initial distancet 1 is the initial time

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FORMULA FOR SPEED V = d 2 – d 1 V = d 2 – d 1 t 2 – t 1 t 2 – t 1 v = speed (velocity) – measured in m/s or km/h v = speed (velocity) – measured in m/s or km/h d = change in distance – measured in mm, cm, m, km d = change in distance – measured in mm, cm, m, km t = change in time – measured in sec, min, hour, year(a) 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? 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: Solution: Δd = 4.5 km, Δ t = 0.62 h, v av = ? v av = Δ d = 4.5 km = 7.3 km / h Δ 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 s. What is the speed of the train in km/h? 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 s. What is the speed of the train in km/h? SOLUTION: SOLUTION: d = 10 km, t = s, v = ? t = s = h v = d = 10 km = 92 km/h 3600 s t 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. 3) Same information of 2 but the question asked for m/s instead of km/h. SOLUTION: SOLUTION: d = 10 km, t = s, v = ? d = 10 km x 1000 m = m v = d = m = m/s 1 km t s The train is traveling at 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? 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: SOLUTION: Δ d = 45 km, v av = 20 km/h, Δ t = ? Rearrange Formula for t. Δ t = Δ d = 45 km = 2.3 h v av 20 km/h Kira should be able t make the trip in 2.3 h.

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PRACTICE Text page 358: #1, 3, 4, 5, 6, 8, 9, 10a, 11a,b Text page 358: #1, 3, 4, 5, 6, 8, 9, 10a, 11a,b Text page 376: #4, 5, 8, 9, 10 Text page 376: #4, 5, 8, 9, 10 Average Speed Worksheet (9.5b,d) Average Speed Worksheet (9.5b,d) Homework check tomorrow

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