Speed velocity and acceleration 1 Both Mr Rabbit

Speed, velocity and acceleration

1 Both Mr Rabbit and Mr Tortoise took the same round trip, but Mr Rabbit slept & returned later.

Who runs faster? Me, as I spent less time on the trip. No, I travelled longer distance every minute. Comment on their argument.

2 A boy has been missing in a forest for 2 hours. O scale = 1 cm : 5 km radius = 8 km (a) If he walks at a speed of 4 km h– 1, try to locate his possible positions on the map.

2 A boy has been missing in a forest for 2 hours. O scale = 1 cm : 5 km radius = 8 km (b) What else is important to spot the boy? The direction in which he has been walking.

1 Speed How can we describe how fast an object moves? E. g. A car on Tolo Highway travels 90 km in 1 hour. We say that the car travels at a speed of 90 km h– 1.

1 Speed How can we describe how fast an object moves? Speed is a measure of how fast something moves. Speed = distance travelled per unit of time SI unit: m s– 1 or km h– 1 (for long distances)

1 Speed a Average speed A car travels at 50 km h– 1, slows down to 0 km h– 1, and speeds up again to 60 km h– 1. Its average speed over the whole journey overall distance travelled = total time of travel

1 Speed a Average speed does not tell the variations during the journey. On most trips, the speed at any instant is often different from the average speed.

1 Speed b Instantaneous speed = speed at any instant The word ‘speed’ alone instantaneous speed Instantaneous speed distance travelled in an extremely short time interval Simulation

1 Speed b Instantaneous speed Speedometer tells the car’s speed at any instant!

2 Velocity is. . . a speed in a given direction or rate of change of displacement. direction velocity magnitude (speed) a vector quantity

2 Velocity a Speed with direction MTR drivers concern speed only. speed = 90 km h– 1 Pilots concern velocity (direction & speed). speed = 300 km h– 1 direction = west

2 Velocity b Average velocity overall displacement Average velocity = total time of travel direction of overall direction of velocity = displacement

2 Velocity c Instantaneous velocity The velocity at any instant is called instantaneous velocity. If a car moves at a constant velocity. . . … its average and instantaneous velocities have the same value.

Q 1 The world record. . . The world record of women 100 -m race is 10. 49 s. What is the average speed? ( 100 ) Average speed = 10. 49 = 9. 53 m s– 1 or 34. 3 km h– 1

Q 2 In an orienteering event. . . In an orienteering event, Maria and Karen reach their control points at the same time. Maria, 10: 30 am start, 10: 00 am Karen, 10: 30 am Who runs in a higher average velocity?

Q 2 In an orienteering event. . . Who runs in a higher average velocity? A Maria. B Karen. C Undetermined since their paths are unknown. D Incomparable since they run along different directions.

Q 3 True or false: Average speed of an object average velocity. magnitude of its (T/F) Note: The distance travelled is equal to magnitude of displacement only if it is a straight-line motion. Speed is usually larger than the magnitude of velocity.

Q 4 True or false: A man takes a walk starting from rest and ending at rest. It is possible for him to attain an average speed of 5 km h– 1 but he never goes faster than 5 km h– 1. (T/F)

3 Acceleration When a car moves faster and faster, its speed is increasing (velocity changed).

3 Acceleration When a car moves slower and slower, its speed is decreasing (velocity changed).

3 Acceleration When a car changes direction, its velocity changes too.

3 Acceleration measures the change in velocity direction speed Acceleration = velocity per unit time overall change in velocity = total time taken Unit: m s– 1 / s = m s– 2 vector quantity

3 Acceleration If a car accelerates at 2 m s– 2, what does that mean? v=0 t=0 1 m t = 1 s v = 2 m s– 1, v = 2 m s– 1 3 m t = 2 s v = 4 m s– 1, v = 2 m s– 1 5 m t=3 s v = 6 m s– 1, v = 2 m s– 1

Example 1 Airport Express takes 0. 35 h to go from HK station to Airport station (34 km). Ave. speed = 34 km/0. 35 h = 97 km h– 1 Complete table. HK Kln Tsing Yi Kln Tsing Yi Airport Distance between stations / km 2. 6 8. 9 (a) Journey time between stations / s 153 (b) 762 Ave. speed between stations / km h– 1 (c) 90 105

Example 1 (b) Kln Tsing Yi: Time = distance / ave. speed = 8. 9 / 90 = 0. 0989 h = 356 s HK Kln Tsing Yi Kln Tsing Yi Airport Distance between stations / km 2. 6 8. 9 (a) Journey time between stations / s 153 (b) 762 Ave. speed between stations / km h– 1 (c) 90 105

Example 1 (a) Tsing Yi Airport: Distance = ave. speed time = 105 12. 7 = 22. 2 km HK Kln Tsing Yi Kln Distance between stations / km Journey time between stations / s Ave. speed between stations / km h– 1 2. 6 8. 9 762 s = (762/3600) 153 (b) h = 12. 7 h (c) 90 Tsing Yi Airport (a) 762 105

(c) Example 1 HK Kln: Ave. speed = distance / time = 2. 6 / 0. 0425 = 61. 2 km HK Kln Tsing Yi Kln Distance between stations / km 2. 6 Journey time between stations / s 153 Ave. speed between stations / km h– 1 (c) 8. 9 Tsing Yi Airport (a) (b) 762 153 s = (153/3600) h =90 0. 0425 h 105

Example 2 A man walks from A to B at 1 km h– 1, and returns at 2 km h– 1. A 1 km h– 1 B 2 km h– 1 Average speed for the whole trip = ?

Example 2 A 1 km h– 1 B 2 km h– 1 Suppose AB = 1 km whole journey = 2 km Time for whole trip = = 1 h + 0. 5 h = 1. 5 h Ave. speed = distance / time = 2/1. 5 1. 33 km h– 1

Example 3 A car travels 7 km north and then 3 km west in 10 minutes. Find (a) average speed, Ave. speed distance travelled = time taken = C (7 + 3) km = 60 km h– 1 (10/60) h 3 km B 7 km A

Example 3 A car travels 7 km north and then 3 km west in 10 minutes. Find (b) ave. velocity? C 3 km B AC = 7 km = 7. 62 km tan = 3/7 =23. 2 o A

Example 3 A car travels 7 km north and then 3 km west in 10 minutes. Find (b) ave. velocity? AC = 7. 62 km, =23. 2 o C 3 km B Size of ave. velocity = displacement time 7. 62 km = (10/60) h = 45. 7 km h– 1 Ave. velocity is 45. 7 km h– 1, 23. 2° north of west. 7 km A

Example 4 The Ferrari 348 can go from rest to 100 km h– 1 in 5. 6 s. What is its ave. acceleration (in m s– 2)? Ave. acceleration 100 km h– 1 (100/3. 6) m s– 1 = = 5. 6 s = 4. 96 m s– 2

Q 1 A running student. . . A running student is slowing down in front of a teacher. +ve With reference to the sign convention, Velocity of student: positive / negative Acceleration of student: positive / negative

Q 2 When time is measured. . . Unit of time: hour (h) Unit of distance/displacement: kilometer (km) Quantity Unit Scalar/Vector Speed ______ km h– 1 _____ scalar Velocity ______ km h– 1 _____ vector Change in velocity ______ km h– 1 km h– 2 ______ vector _____ Acceleration

Q 3 In 2. 5 s, a car speeds up. . . In 2. 5 s, a car speeds up from 60 km h– 1 to 65 km h– 1. . . …while a bicycle goes from rest to 5 km h– 1. Which one has the greater acceleration? They have the same acceleration!

Q 4 A car is moving in positive. . . A car is moving in +ve direction. What happens if it moves under a ve acceleration? The car will slow down. What happens if it moves under a ve deceleration? The car will move in +ve direction with increasing speed.