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 Distance – the total length that an object has travelled. 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 A scalar is a quantity that can be completely described by one value: the magnitude (size).

12.1 Measuring Motion A vector has both distance and direction. 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.

Comment on their argument. 12.1 Measuring Motion Who runs faster? No, I travelled longer distance every minute. Me, as I spent less time on the trip. Comment on their argument.

Speed E.g. A car on Jal el Dib Highway travels 90 km in 1 hour. 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 = 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 or km/h (for long distances)

Speed Distance vs. Time B Distance (m) A 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 overall distance travelled 50 km + 60 km = total time of travel 3 h = 36.7 km/h

Average Speed Calculate the average speed of the car at point A and point B Distance (m) Time (s)

Distance(m) Time (s)

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

Speedometer tells the car’s speed at any instant! 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. Average speed for the whole trip = ?

Avg. speed = distance / time Q2 1 km / h A B 2 km / h Suppose AB = 1 km  whole journey = 2 km Time for whole trip = = 1 h + 0.5 h = 1.5 h Avg. speed = distance / time = 1.33 km/h = 2/1.5

rate of change of displacement or 12.2 Velocity Velocity is... rate of change of displacement or a speed in a given direction. direction a vector quantity velocity 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 distance Direction of 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? Answer? They BOTH are! Rabbit – instantaneous velocity at the beginning and end of the race Tortoise – average velocity over the whole race Answer? They BOTH are!

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 Jounieh  Antelias Antelias Airport Distance between cities/ km Travel time btw cities/ min Avg. speed btw cities/ km/h 30 15.4 (a) 17 (b) 16 (c) 90 55

Example 1 (a) Antelias  Airport: Distance = avg. speed  time = 55 km/h  0.267 h = 14.7 km Batroun Jounieh Jounieh  Antelias Antelias  Airport Distance between cities/ km Travel time btw cities/ min Avg. speed btw cities/ km/h 30 15.4 (a) 17 (b) 16 (c) 90 55 = (16min/60min/h) = 0.267 h

Example 1 (b) Jounieh  Antelias: Time = distance / avg. speed = 15.4km/90km/h = 0.171 h =10.3min Batroun Jounieh Jounieh  Antelias Antelias  Airport Distance between stations / km Distance between stations / km 30 15.4 (14.7) Travel time btw stations / min Journey time between stations / s 17 (b) 16 Avg. speed btw stations / km/h Ave. speed between stations / km h–1 (c) 90 55

Example 1 (c) Batroun  Jounieh: Avg. speed = distance / time = 30km/ 0.283h = 106 km/h Batroun Jounieh Jounieh  Antelias Antelias  Airport Distance between stations / km Time between stations / min Ave. speed btw stations / km/h 30.0 15.4 (14.7) 17 (10.3) 16 (c) 90 55 = (17min/60min/h) = 0.283 h

Example 1 (30+15.4+14.7)km Total distance Avg. speed = (d) What was the total average speed for the whole trip? (30+15.4+14.7)km Total distance Avg. speed = (17+10.3+16)min/60min/h Total time 60.1km = 83.3 km/h 0.722h Batroun Jounieh Jounieh  Antelias Antelias Airport Distance between cities/ km Travel time btw cities/ min Avg. speed btw cities/ km/h 30 15.4 (14.7) 17 (10.3) 16 (106) 90 55

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 vector quantity Unit: m s–1 / s = m s–2

Acceleration t = 0 v = 0 t = 1 s v = 2 m/s, v = 2 m/s t = 2 s 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 2 m t = 2 s v = 4 m/s, v = 2 m/s 4 m t = 3 s v = 6 m/s, v = 2 m/s 6 m

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 = 1000m/3600s 1km/h = 1m/3.6s 100 km/h 5.6 s (100/3.6) m/s 5.6 s = = 4.96 m/s2

Speed Graph

Acceleration Graph What is: a) The acceleration between O and A? 25m/s 110s 45s 90s (25m/s)/45s = 0.56m/s2 (-25m/s)/20s = -1.25m/s2 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 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

They have the same acceleration! 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) Unit of distance: kilometer (km) (or s if using small numbers) Unit of distance: kilometer (km) (or m if using small numbers) Quantity Unit Scalar/Vector Speed ______ _____ Velocity ______ _____ Change in velocity ______ _____ Acceleration ______ _____ km/h scalar km/h vector km/h vector km/h2 vector

The End

Distance(m) 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 Jounieh  Beirut dis. Beirut dis. Airport Distance between stations / km Travel time btw stations / s Avg. speed btw stations / km/h 2.6 8.9 (a) 153 (b) 762 (c) 90 105 Complete the table.