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Chapter 12 What is motion? Describing Motion Point of reference: An object or group of objects that is considered to be stationary Point of Reference From the man standing outside’s perspective, what is happening to the bus? From the bus driver’s perspective, what is happening to the man? Point of Reference From this driver’s perspective, is he standing still, moving forward or backwards? What about the car in his rear view mirror? The buildings in front of him? 12.1 Measuring Motion n Distance – the total length that an object has travelled. n Displacement – the distance and direction from the starting point to the ending point. Path taken is not important. 12.1 Measuring Motion Displacement distance displacement 12.1 Measuring Motion How do we accurately communicate distance and displacement? 12.1 Measuring Motion n A scalar is a quantity that can be completely described by one value: the magnitude (size). 12.1 Measuring Motion n A vector has both distance and direction. n If you walk five meters east, your displacement can be represented by a 5 cm arrow pointing to the east. 12.1 Measuring Motion Both Mr. Rabbit and Mr. Tortoise took the same round trip, but Mr. Rabbit slept & returned later. 12.1 Measuring Motion Who runs faster? No, I travelled Me, as I spent longer distance every less time on the minute. trip. Comment on their argument. Speed How can we describe how fast an object moves? E.g. A car on Jal el Dib Highway travels 90 km in 1 hour. We say that the car travels at a speed of 90 km/h. 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 or km/h (for long distances) Speed Distance vs Time Distance vs.Time 12 10 B Distance (m) 8 6 4 A 2 0 0 1 2 3 4 5 Time (s) Speed 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. Speed Average speed A car travels at 50 km/h, for an hour slows down to 0 km/h, for an hour and speeds up to 60 km/h for another hour. Its average speed over the whole journey 50 distance km overall km + 60 travelled = total time of travel 3h = 36.7 km/h Average Speed Calculate the average speed of the car at point A and point B Distance vs. Time 35 30 B 25 Distance (m) 20 15 10 A 5 0 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 Time (s) Distance vs. Time 140 120 100 Distance(m) 80 60 40 20 0 0 1 2 3 4 5 Time (s) Speed Instantaneous speed Instantaneous speed = speed at any instant The word ‘speed’ alone instantaneous speed Instantaneous speed distance travelled in an extremely short time interval Speed Instantaneous speed Speedometer tells the car’s speed at any instant! Q1 The world record... The world record of women 100-m race is 10.49 s. What is the average speed? ( 100 m ) Average speed = 10.49 s = 9.53 m/s or 34.3 km/h (9.53 m/s x 3600 s/h = 34308 m/h = 34.3 km/h ) Q2 A man walks from A to B at 1 km/h and returns at 2 km/h. A 1 km/h B 2 km/h Average speed for the whole trip = ? Q2 A 1 km / h B 2 km / h Suppose AB = 1 km whole journey = 2 km 1 km 1 km Time for whole trip = 1 km/h 2 km/h = 1 h + 0.5 h = 1.5 h Avg. speed = distance / time = 1.33 km/h = 2/1.5 12.2 Velocity Velocity is... rate of change of displacement or a speed in a given direction. direction velocity a vector quantity magnitude (speed) Velocity Speed with direction A subway driver’s concern is speed only. speed = 90 km h–1 A pilot’s concern is velocity (direction & speed). speed = 300 km/h direction = west Velocity Average velocity overall distance Average velocity = total time of travel direction of overall Direction of velocity = distance Velocity 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. So Who is Faster? Rabbit – instantaneous velocity Answer? They Tortoise – average velocity over the at the beginning and BOTH are! end of the race whole race Q1 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 at a higher average velocity? Q1 In an orienteering event... Who runs at a higher average velocity? A Maria. B Karen. C Undetermined since their paths are unknown. D Incomparable since they run along different directions. Example 1 A car travels from Batroun to the airport in Beirut. Use the formula, s=d/t to calculate a, b and c in the following table: Batroun Jounieh Antelias Jounieh Antelias Airport Distance between 30 15.4 (a) cities/ km Travel time btw 17 (b) 16 cities/ min Avg. speed btw (c) 90 55 cities/ km/h Example 1 (a) Antelias Airport: Distance = avg. speed time = 55 km/h 0.267 h = 14.7 km Batroun Jounieh Antelias Jounieh Antelias Airport Distance between 30 15.4 (a) cities/ km = (16min/60min/h) = h Travel time btw 0.26717 (b) 16 cities/ min Avg. speed btw (c) 90 55 cities/ km/h Example 1 (b) Jounieh Antelias: Time = distance / avg. speed = 15.4km/90km/h = 0.171 h =10.3min Batroun Jounieh Antelias Jounieh Antelias Airport Distance between 30 15.4 (14.7) stations / km Travel time btw Journey time 17 (b) 16 between min stations /stations / s Avg. speed btw Ave. between (c) 90 55 stations / km/h–1 km h Example 1 (c) Batroun Jounieh: Avg. speed = distance / time = 30km/ 0.283h = 106 km/h Batroun Jounieh Antelias Jounieh Antelias Airport Distance between 30.0 15.4 (14.7) stations / km Time between 17 (10.3) 16 stations / min = (17min/60min/h) Ave. speed btw (c) =90 0.283 h 55 stations / km/h Example 1 (d) What was the total average speed for the whole trip? Total distance (30+15.4+14.7)km Avg. speed = 60.1km (17+10.3+16)min/60min/h Total time = 83.3 km/h 0.722h Batroun Jounieh Antelias Jounieh Antelias Airport Distance between 30 15.4 (14.7) cities/ km Travel time btw 17 (10.3) 16 cities/ min Avg. speed btw (106) 90 55 cities/ km/h Acceleration When a car moves faster and faster, its speed is increasing (velocity changed). Acceleration When a car moves slower and slower, its speed is decreasing (velocity changed). Acceleration When a car changes direction, its velocity changes too. Acceleration 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 Acceleration If a car accelerates at 2 m/s2, what does that mean? t=0 v=0 t = 1 s v = 2 m/s, v = 2 m/s 2m t = 2 s v = 4 m/s, v = 2 m/s 4m t=3s v = 6 m/s, 6m v = 2 m/s Acceleration The Ferrari 348 can go from rest to 100 km/h in 5.6 s. What is its avg. acceleration (in m/s2)? Avg. acceleration 1km/h = 1km/h = 1m/3.6s 1000m/3600s 100 km/h (100/3.6) m/s = = 5.6 s 5.6 s = 4.96 m/s2 Speed Graph Acceleration Graph 25m/s 45s 90s 110s What is: a) The acceleration between O and A? b) The acceleration between A and B? c) The acceleration between B and C? Q1 A running student... A running student +ve 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 In 2.5 s, a car speeds up... In 2.5 s, a car speeds up from 60 km/h to 65 km/h... …while in 2.5 s, a bicycle goes from rest to 5 km/h. Which one has the greater acceleration? They have the same acceleration! Q3 A car is moving in a positive direction... A car is moving in a +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. Note Unit of time: hour (h) (or s if using small numbers) Unit of distance: kilometer (km) (or m if using small numbers) Quantity Unit Scalar/Vector Speed km/h ______ scalar _____ Velocity km/h ______ vector _____ Change in velocity ______ km/h _____ vector Acceleration km/h2 ______ vector _____ The End Distance vs. Time 140 120 100 Distance(m) 80 60 40 20 0 0 1 2 3 4 5 Time (s) Example 1 Airport Express takes 0.35 h to go from Batroun to the Airport (34 km). Avg. speed = 34 km/0.35 h = 97 km/h Batroun Jounieh Beirut dis. Complete the table. Jounieh Beirut dis. Airport Distance between 2.6 8.9 (a) stations / km Travel time btw 153 (b) 762 stations / s Avg. speed btw (c) 90 105 stations / km/h

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