Ch. 10: Motion Unit Integrated Science I Motion in One Dimension.

Ch. 10: Motion UnitCh. 10: Motion UnitIntegrated Science IIntegrated Science I

Motion in One DimensionMotion in One Dimension

Motion in One DimensionMotion in One Dimension

One-dimensional motion is the simplest form of One-dimensional motion is the simplest form of motion. To picture this form of motion, think of motion. To picture this form of motion, think of a train moving along a straight track.a train moving along a straight track.

More motion…More motion…

Motion takes place over time and Motion takes place over time and depends on the frame of reference.depends on the frame of reference.

The frame of reference is a system for The frame of reference is a system for specifying the precise location of objects specifying the precise location of objects in space and time.in space and time.

If an object is not moving, it has a fixed If an object is not moving, it has a fixed frame of reference.frame of reference.

DisplacementDisplacement

Displacement is the change in position of Displacement is the change in position of an object.an object.

To find Displacement:To find Displacement: Change in position = final position – start Change in position = final position – start

positionposition

Or Or Δ Δ x = xx = xff – x – xi i ((ΔΔ = change) = change)

Displacement can also be used verticallyDisplacement can also be used vertically Such as Such as ΔΔy = yy = yff- y- yii

DISPLACEMENT PRACTICE DISPLACEMENT PRACTICE PROBLEM!PROBLEM!

An ant walking on a ruler begins at the 10 cm An ant walking on a ruler begins at the 10 cm mark, and stops walking at the 50 cm mark. mark, and stops walking at the 50 cm mark. What is the ant’s displacement?What is the ant’s displacement?

Displacement = xDisplacement = xff – x – xii, 50 cm – 10 cm = 40 cm. , 50 cm – 10 cm = 40 cm.

Answer! 40 cm. Final position = 50 cm, initial Answer! 40 cm. Final position = 50 cm, initial position = 10 cm. position = 10 cm.

Tricky business!Tricky business!

Displacement is not alwaysDisplacement is not always equal to the distance traveled!equal to the distance traveled! FOR EXAMPLE… FOR EXAMPLE… A dog stands up from his bed, walks 5 meters, A dog stands up from his bed, walks 5 meters,

stops, walks back, and goes back to sleep. The stops, walks back, and goes back to sleep. The dog’s displacement is dog’s displacement is ZEROZERO, because his final , because his final position and his initial position were both equal, position and his initial position were both equal, being as they were the same spot. Subtracting two being as they were the same spot. Subtracting two equal numbers gets you zero!equal numbers gets you zero!

Can you think of any other examples when Can you think of any other examples when displacement is zero?displacement is zero?

Displacement can be positive or Displacement can be positive or negativenegative

Movement to the right, or east, is Movement to the right, or east, is considered positive.considered positive.

Movement to the left, or west, is Movement to the left, or west, is considered negative.considered negative.

When using displacement vertically, When using displacement vertically, upward or northern movement is positive upward or northern movement is positive and downward or southern movement is and downward or southern movement is negative.negative.

VELOCITYVELOCITY Average velocity: Average velocity: the total displacement the total displacement

divided by the time the displacement occurred.divided by the time the displacement occurred. The label of velocity is meters per second, or The label of velocity is meters per second, or

m/sm/s.. Average velocity = change in position / change in time Average velocity = change in position / change in time

VVavgavg = = (x(xff – x – xii) ) / (t/ (tff – t – tii))

Velocity is not the same Velocity is not the same as speed!as speed!

Average speedAverage speed distance traveled / time of traveldistance traveled / time of travel

Average velocityAverage velocity displacement / time of traveldisplacement / time of travel

The main difference between the two is The main difference between the two is that velocity values give a direction, while that velocity values give a direction, while speed does not.speed does not.

Why Velocity is Important Why Velocity is Important When Predicting WeatherWhen Predicting Weather What is What is

Important to Important to Know When a Know When a Storm is Storm is Coming?Coming? How strong How strong How How fastfast it is it is

comingcoming From what From what

directiondirection it is it is comingcoming

AVERAGE VELOCITY AVERAGE VELOCITY PRACTICE PROBLEM!PRACTICE PROBLEM!

A student walks 10 km east to school in A student walks 10 km east to school in 2.3 hours. What is his average velocity?2.3 hours. What is his average velocity?

VVavg avg = = ΔΔxx//ΔΔtt = 10 km/2.3 hrs = 4.35 km/hr = 10 km/2.3 hrs = 4.35 km/hr

ANSWER. 4.35 km/hr to ANSWER. 4.35 km/hr to the east! the east!

MORE AVERAGE MORE AVERAGE VELOCITY PRACTICEVELOCITY PRACTICE Coach Ross paces back and forth along the Coach Ross paces back and forth along the

sidelines. At each marked position, the coach sidelines. At each marked position, the coach makes a "U-turn" and moves in the opposite makes a "U-turn" and moves in the opposite direction. In other words, the coach moves from direction. In other words, the coach moves from position A to B to C to D. position A to B to C to D.

What is the Coach Ross’s average speed and What is the Coach Ross’s average speed and average velocity? average velocity?

Let’s Do Average Speed Let’s Do Average Speed FirstFirst Average Speed = distance/timeAverage Speed = distance/time

A to B = _______ yd, ________ minA to B = _______ yd, ________ min B to C = _______ yd, ________ minB to C = _______ yd, ________ min C to D = _______ yd, ________ minC to D = _______ yd, ________ min

Total Distance = ___________ ydTotal Distance = ___________ yd Total Time = ______________ minTotal Time = ______________ min Average Speed = __________ yd/minAverage Speed = __________ yd/min

352040

9510

334

9.5

Now to Find Average Now to Find Average VelocityVelocity

Average Velocity = displacement/timeAverage Velocity = displacement/time Displacement = ________ yd to the ____Displacement = ________ yd to the ____ Time = __________ minTime = __________ min Average Velocity = ____________yd min Average Velocity = ____________yd min

to the ___________to the ___________

55 west

10

5.5west

Velocity can be interpreted Velocity can be interpreted graphicallygraphically

Slope = rise / runSlope = rise / run Change in vertical Change in vertical

coordinates / change coordinates / change in horizontal in horizontal coordinates coordinates

Position Position versus time versus time

graph graph example…example…

Velocity graphs show Velocity graphs show straight lines straight lines

Object 1…moving at a Object 1…moving at a constant positive constant positive velocity.velocity. Example: a car on cruise Example: a car on cruise

control traveling at 55 mph.control traveling at 55 mph. Position is changing the Position is changing the

same amount each second same amount each second away from the startaway from the start

Object 2…at rest. Object 2…at rest. Example: a parked car.Example: a parked car. Position does not change Position does not change

each secondeach second Object 3…moving with a Object 3…moving with a

constant negative constant negative velocityvelocity Example: a car in cruise Example: a car in cruise

control in REVERSE going control in REVERSE going 20 mph.20 mph.

Position is changing the Position is changing the same amount each second same amount each second towards the starttowards the start

Instantaneous VelocityInstantaneous Velocity Definition: the velocity of an Definition: the velocity of an

object at some instant or at object at some instant or at a specific point in the a specific point in the object’s pathobject’s path

Picking one point on a Picking one point on a graph shows instantaneous graph shows instantaneous velocityvelocity

For example, you look at For example, you look at your speedometer for your your speedometer for your speed at that instant speed at that instant

Acceleration!Acceleration!

Acceleration is the rate at which velocity Acceleration is the rate at which velocity changes over time.changes over time.

An object accelerates if its speed, An object accelerates if its speed, direction, or both change.direction, or both change.

Average acceleration = change in Average acceleration = change in velocity / time required for changevelocity / time required for change AAavgavg = (v = (vff – v – vii) / (t) / (tff – t– tii))

Labeled as m/sLabeled as m/s²²

AVERAGE ACCELEARTION AVERAGE ACCELEARTION PRACTICE PROBLEM!PRACTICE PROBLEM!

A roller coaster starts at rest and speeds A roller coaster starts at rest and speeds up to 50 m/s over the course of 17 up to 50 m/s over the course of 17 seconds. What is the average acceleration seconds. What is the average acceleration of the roller coaster?of the roller coaster?

Show your work!Show your work! AAavgavg = = ΔΔv/v/ΔΔt t Velocity final = __________Velocity final = __________ Velocity start = __________Velocity start = __________ Time = ________________Time = ________________

(50 m/s) / (17 sec) = 2.9 m/s²(50 m/s) / (17 sec) = 2.9 m/s² ANSWER. 2.9 m/s²ANSWER. 2.9 m/s²

50 m/s0 m/s

17 seconds

Acceleration can be read Acceleration can be read as a graph tooas a graph too

Acceleration = a curved lineAcceleration = a curved line *Remember, velocity is *Remember, velocity is

a a straight linestraight line

The graph to the right The graph to the right shows a car starting to slow shows a car starting to slow down then slamming on down then slamming on their brakes to slow down their brakes to slow down quickly.quickly.