Speed, velocity and acceleration

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

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

2 A boy has been missing in a forest for 2 hours. radius = 8 km scale = 1 cm : 5 km O (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. radius = 8 km scale = 1 cm : 5 km O (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.

Speed = distance travelled per unit of time 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)

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 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.

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

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

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

a Speed with direction MTR drivers concern speed only. 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

b Average velocity overall displacement Average velocity = total time of travel direction of overall displacement direction of 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.

Q1 The world record... The world record of women 100-m race is 10.49 s. What is the average speed? ( ) Average speed = 10.49 100 = 9.53 m s–1 or 34.3 km h–1

Q2 In an orienteering event... In an orienteering event, Maria and Karen reach their control points at the same time. start, 10:00 am Maria, 10:30 am Karen, 10:30 am Who runs in a higher average velocity?

Q2 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.

Q3 True or false: Average speed of an object  magnitude of its average velocity. (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.

Q4 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 Acceleration measures the change in velocity direction speed Acceleration = velocity per unit time overall change in velocity = total time taken vector quantity Unit: m s–1 / s = m s–2

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

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 Kln  Tsing Yi Tsing Yi  Airport Distance between stations / km Journey time between stations / s Ave. speed between stations / km h–1 2.6 8.9 (a) 153 (b) 762 (c) 90 105

Example 1 (b) Kln  Tsing Yi: Time = distance / ave. speed = 8.9 / 90 = 0.0989 h = 356 s HK  Kln Kln  Tsing Yi Tsing Yi  Airport Distance between stations / km Journey time between stations / s Ave. speed between stations / km h–1 2.6 8.9 (a) 153 (b) 762 (c) 90 105

Example 1 (a) Tsing Yi  Airport: Distance = ave. speed  time = 105  12.7 = 22.2 km HK  Kln Kln  Tsing Yi Tsing Yi  Airport Distance between stations / km Journey time between stations / s Ave. speed between stations / km h–1 2.6 8.9 (a) 153 (b) 762 (c) 90 105 762 s = (762/3600) h = 12.7 h

Example 1 (c) HK  Kln: Ave. speed = distance / time = 2.6 / 0.0425 = 61.2 km HK  Kln Kln  Tsing Yi Tsing Yi  Airport Distance between stations / km Journey time between stations / s Ave. speed between stations / km h–1 2.6 8.9 (a) 153 (b) 762 (c) 90 105 153 s = (153/3600) h = 0.0425 h

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

Ave. speed = distance / time Example 2 1 km h–1 A 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 = 3 km C B distance travelled time taken 7 km = (7 + 3) km (10/60) h = 60 km h–1 A

Example 3 A car travels 7 km north and then 3 km west in 10 minutes. Find (b) ave. velocity? 3 km C B AC = 7 km = 7.62 km  tan q = 3/7  q =23.2o A

Example 3 A car travels 7 km north and then 3 km west in 10 minutes. Find (b) ave. velocity? 3 km AC = 7.62 km, q =23.2o C B Size of ave. velocity = displacement 7.62 km 7 km = time (10/60) h  = 45.7 km h–1 Ave. velocity is 45.7 km h–1, 23.2° north of west. 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 5.6 s (100/3.6) m s–1 5.6 s = = 4.96 m s–2

Q1 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

Q2 When time is measured... Unit of time: hour (h) Unit of distance/displacement: kilometer (km) Quantity Unit Scalar/Vector Speed ______ _____ Velocity ______ _____ Change in velocity ______ _____ Acceleration ______ _____ km h–1 scalar km h–1 vector km h–1 vector km h–2 vector

They have the same acceleration! Q3 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!

Q4 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.