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## Speed, velocity and acceleration

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**1 Both Mr Rabbit and Mr Tortoise took the same round trip,**but Mr Rabbit slept & returned later.**Who runs faster?**No, I travelled longer distance every minute. Me, as I spent less time on the trip. Comment on their their argument.**radius = 8 km**2 A boy has been missing in a forest for 2 hours. 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.**radius = 8 km**2 A boy has been missing in a forest for 2 hours. 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 ata speedof 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 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 Instantaneous speed The word ‘speed’ alone instantaneous speed Instantaneous speed distance travelled inan extremely short time interval Simulation**1 Speed**b Instantaneous speed Speedometer tells the car’s speed at any instant!**direction**magnitude (speed) 2 Velocity Velocity is... a speed in a given direction or rate of change of displacement. a vector quantity velocity**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 displacement direction of velocity =**2 Velocity**c Instantaneous velocity The velocity atany instant is calledinstantaneous velocity. If a car moves at a constant velocity... … its average and instantaneous velocities have the same value.**( )**Average speed = 10.49 Q1 The world record... The world record of women 100-m race is 10.49 s. What is the average speed? 100 = 9.53 m s–1or 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 alongdifferent directions.**Q3 True or false:**Average speed of an object magnitude of its average velocity. (T/F) Note: The distance travelled is equal tomagnitude 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 andending at rest. It is possible for him to attain an averagespeed of 5 km h–1 but he never goes faster than5 km h–1. (T/F)**3 Acceleration**When a car moves faster and faster, its speed is increasing (velocitychanged).**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.**direction**speed 3 Acceleration Acceleration measures the change in velocity Acceleration = velocity per unit time overall change in velocity = total time taken vector quantity Unit: m s–1 / s = m s–2**3 Acceleration**If a car accelerates at 2 m s–2, what does that mean? v = 0 t = 0 v = 2 m s–1, v = 2 m s–1 t = 1 s 1 m v = 4 m s–1, v = 2 m s–1 t = 2 s 3 m t = 3 s v = 6 m s–1, v = 2 m s–1 5 m**Kln Tsing Yi**Tsing Yi Airport HK Kln 2.6 8.9 Distance between stations / km (a) 153 Journey time between stations / s (b) 762 Ave. speed between stations / km h–1 (c) 90 105 Example 1 Airport Expresstakes 0.35 h to go fromHK station to Airport station (34 km). Ave. speed = 34 km/0.35 h =97 kmh–1 Complete table.**Kln Tsing Yi**Tsing Yi Airport HK Kln 2.6 8.9 Distance between stations / km (a) 153 Journey time between stations / s (b) 762 Ave. speed between stations / km h–1 (c) 90 105 Example 1 (b) Kln Tsing Yi: distance/ ave. speed Time = = 8.9/ 90 = 0.0989 h = 356 s**Kln Tsing Yi**Tsing Yi Airport HK Kln 2.6 8.9 Distance between stations / km (a) 153 Journey time between stations / s (b) 762 Ave. speed between stations / km h–1 (c) 90 105 Example 1 (a) Tsing Yi Airport: Distance = ave. speedtime = 22.2 km = 10512.7 762 s = (762/3600) h = 12.7 h**Kln Tsing Yi**Tsing Yi Airport HK Kln 2.6 8.9 Distance between stations / km (a) 153 Journey time between stations / s (b) 762 Ave. speed between stations / km h–1 (c) 90 105 Example 1 (c) HK Kln: distance/ time Ave. speed = = 2.6/ 0.0425 = 61.2 km 153 s = (153/3600) h = 0.0425 h**2 km h–1**Example 2 A man walks from A to B at 1 km h–1, and returns at 2 km h–1. 1 kmh–1 A B Average speed for thewhole trip = ?**2 km h–1**Example 2 1 kmh–1 A B whole journey = 2 km Suppose AB = 1 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**(7 + 3) km**= (10/60) h Example 3 A car travels 7 km north and then 3 km west in 10 minutes. Find (a) average speed, Ave. speed = 3 km B C distance travelled time taken 7 km = 60 kmh–1 A****Example 3 A car travels 7 km north and then 3 km west in 10 minutes. Find (b) ave. velocity? 3 km B C AC = 7 km = 7.62 km q =23.2o tan q = 3/7 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 B C 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**100 km h–1**5.6 s (100/3.6) m s–1 = 5.6 s Example 4 The Ferrari 348 can go from rest to 100 km h–1in 5.6 s. What is its ave.acceleration (in m s–2)? Ave. acceleration = = 4.96 m s–2**+ve**Q1 A running student... A running student is slowing down in front of a teacher. 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**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 onehas 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 veacceleration? The car will slow down. What happens if it moves undera ve deceleration? The car will move in +ve direction with increasing speed.