Ch.2 Speed (速率) & Velocity (速度)
2.1 Introduction ＊ Different objects move with different speeds. For example: ＊ Speed of sound = 340 m s-1 ＊ Speed of light = 3 × 108 m s-1 (maximum value)
2.2 Average speed (平均速率) ＊ measures how fast an object moves. ＊ is a scalar (無向量). ＊ unit is m s-1 or m/s (read as “metre per second”) average speed = distance travelled time taken
Class Exercise 2.1 The world record for the men’s 100 m race is 9.69 s Calculate the average speed of the record holder. (Usain Bolt, 2008 at Beijing)
Average speed = = Class Exercise 2.1 The world record for the men’s 100 m race is 9.69 s Calculate the average speed of the record holder. (Usain Bolt, 2008 at Beijing) Average speed = =
Class Exercise 2.2 The Disneyland Resort Line of MTR system is a 3.5-kilometre single-track railway that runs between Sunny Bay station and Disneyland Resort station. The train takes 6.0 minutes travelling between these two stations. Calculate the average speed of the train.
Class Exercise 2.2 1000 60 9.72 m s-1
Class Exercise 2.3 Tourists can go to Macau by jetfoil. The distance between Hong Kong and Macau is 61 km. The jetfoil will take 55 minutes from Hong Kong to Macau. Calculate the average speed of the jetfoil.
Average speed = = Class Exercise 2.3 Tourists can go to Macau by jetfoil. The distance between Hong Kong and Macau is 61 km. The jetfoil will take 55 minutes from Hong Kong to Macau. Calculate the average speed of the jetfoil. Average speed = =
2.3 Average velocity (平均速度) ＊ measures how fast an object moves with direction. ＊ is a vector (向量). ＊ same direction as the displacement. ＊ unit is m s-1 or m/s (read as “metre per second”) average velocity = displacement time taken
Class Exercise 2.4
No, it is because their direction is not the same. Class Exercise 2.4 No, it is because their direction is not the same.
Class Exercise 2.5
Class Exercise 2.5 Average velocity = =
(i) average speed = average velocity = 50 ÷ 25 = 2 m s-1 (∵ distance = displacement = 50 m)
(ii) the whole trip.
(ii) average speed = distance ÷ time = (50+50) ÷ (25+30) = 1.82 m s-1 (ii) the whole trip. (ii) average speed = distance ÷ time = (50+50) ÷ (25+30) = 1.82 m s-1 average velocity = displacement ÷ time = 0 (∵displacement = 0)
6.5 cm
6.5 cm 1.3 cm distance = (6.5/1.3)(20 m) = 100 m
(b) Mary lives in Block P (b) Mary lives in Block P. She uses 20 s to go from LPSMC to her home after school. Calculate her average velocity.
average velocity = displacement ÷ time = 100 ÷ 20 = 5.0 m s-1 (b) Mary lives in Block P. She uses 20 s to go from LPSMC to her home after school. Calculate her average velocity. average velocity = displacement ÷ time = 100 ÷ 20 = 5.0 m s-1
(c) John is Mary’s brother. He runs from LPSMC back to his home (c) John is Mary’s brother. He runs from LPSMC back to his home. His average velocity is 7 m s-1. Calculate the time taken for his journey.
average velocity = displacement ÷ time 7 = 100 ÷ time ∴ time = 14.2 s (c) John is Mary’s brother. He runs from LPSMC back to his home. His average velocity is 7 m s-1. Calculate the time taken for his journey. average velocity = displacement ÷ time 7 = 100 ÷ time ∴ time = 14.2 s
2.4 Instantaneous velocity (瞬間速度) = Velocity at the particular time = Average velocity when the time interval is very small
100 km/h or 100 km h-1
100 km/h or 100 km h-1 velocity = (100×1000) ÷ (60×60) = 27.8 m s-1
v = 5 m s-1
v = 5 m s-1 v = 10 m s-1
v = 5 m s-1 v = 10 m s-1 v = 18 m s-1
(b) Calculate the average velocity at the time interval (i) between X and Y. (ii) between Y and Z.
velocity = 75 ÷ 10 = 7.5 m s-1 velocity = 135 ÷ 10 = 13.5 m s-1
12 m s-1 (North) 12 m s-1 (East) 12 m s-1 (South) 12 m s-1 (West)
velocity = displacement ÷ time = 0