Relative MotionRelative Motion

Frames of ReferenceFrames of Reference

Object or point from which motion is Object or point from which motion is determineddetermined

Most common is the Most common is the

earthearth Motion is a changeMotion is a change

in in positionposition relativerelative to to

a frame of referencea frame of reference

What is motion?What is motion?

If you are standing in one place, and your If you are standing in one place, and your friend walks by you, are you moving friend walks by you, are you moving relative to your friend?relative to your friend? Is your friend moving relative to you?Is your friend moving relative to you? Is either of you moving relative to the Is either of you moving relative to the

earth?earth?

Answer:Answer:

You are moving relative to your friend, and You are moving relative to your friend, and your friend is moving relative to you!your friend is moving relative to you!

You are not moving relative to the earth, You are not moving relative to the earth, but your friend is. You are both moving but your friend is. You are both moving relative to the sun!relative to the sun!

What is motion?What is motion?

If you and your friend are walking down the hall If you and your friend are walking down the hall together at the same speed, in the same direction, together at the same speed, in the same direction, are you moving relative to your friend?are you moving relative to your friend? Is your friend moving relative Is your friend moving relative

to you?to you? Are either of you moving Are either of you moving

relative to the earth?relative to the earth?

Answer:Answer: You are NOT moving relative to You are NOT moving relative to

your friend, and your friend is NOT your friend, and your friend is NOT moving relative to you. You both moving relative to you. You both are moving relative to the earth.are moving relative to the earth.

Uniform motionUniform motionUniform motion – occurs when an object is moving at a constant speed/ velocity in a straight line.Constant speed/velocity- means that the object is covering the same distance per unit of time.

Scalar – any quantity that is represented by a magnitude and a unit.

Vector – any quantity that is represented by a Magnitude, a unit and a direction.

Distance and DisplacementDistance and Displacement

DistanceDistance (d) (d) is a is a scalarscalar measure of measure of the the actual pathactual path between two between two locations .locations .

It has a magnitude It has a magnitude and a unit.and a unit.

Ex: 50 m, 2.5 hrs.Ex: 50 m, 2.5 hrs.

DisplacementDisplacement (d)(d) is is a a vectorvector measure measure of the of the change in change in positionposition measured measured in a straight line in a straight line from a starting from a starting reference point.reference point.

Ex: 5 m [W]Ex: 5 m [W]

Sign ConventionSign Convention

In physics we In physics we will use a will use a standard set of standard set of signs and signs and directions.directions.

Up, right, east and Up, right, east and north are positive north are positive directions. ( + )directions. ( + )

Down, left, west, Down, left, west, and south are and south are negative negative directions. ( - )directions. ( - )

Distance – total trip d total = d1 + d2 + d3 + d4

d total = 2m + 4m + 2m + 4m

d total = 20 m

Displacement – change in position

d total = +d1 + +d2 + -d3 + -d4

d total = +2m + +4m + -2m + -4m d total = 0 m

SpeedSpeed

Speed = Change in distance ÷ TimeSpeed = Change in distance ÷ Time

ΔΔ d_ d_

V TV T

Example: A car travels 300km in 6 Example: A car travels 300km in 6 hours. What is the speed of the car?hours. What is the speed of the car?

Answer:Answer:

Speed = distance ÷ timeSpeed = distance ÷ time Speed = 300km ÷ 6 hoursSpeed = 300km ÷ 6 hours Speed = 50km/hrSpeed = 50km/hr

More practiceMore practice

1. How far can a plane travel if it flies 1. How far can a plane travel if it flies 800km/hr for 9 hours?800km/hr for 9 hours?

2. How long does it take a ship to go 500 2. How long does it take a ship to go 500 km if it travels at a speed of 50km/hr?km if it travels at a speed of 50km/hr?

AnswerAnswer

1. 1. Δ Δ d d V TV T

ΔΔ d d 800800 9 9

800km 800km ▪ 9hrs = 7200km ▪ 9hrs = 7200km hrhr

AnswerAnswer

2. 2. Δ Δ d d VV T T 500 500 5050 T T

500km ÷ 500km ÷ 50km50km = 10 hrs = 10 hrs hrhr

Instantaneous SpeedInstantaneous Speed

Instantaneous speed Instantaneous speed is speed at is speed at any instant in timeany instant in time..

A speedometer measures speed in A speedometer measures speed in ‘real time’ (the‘real time’ (the instantaneous speed instantaneous speed).).

Average SpeedAverage Speed Average speed Average speed is the average of all is the average of all

instantaneous speeds; found simply instantaneous speeds; found simply by a total distance/total time ratioby a total distance/total time ratio

The The average speedaverage speed of a trip: of a trip:

timeelapsed

distance total speed average

Vavg = d1 + d2 + d3 + d4........

t1 + t2 + t3 + t4 ..........

VelocityVelocity Speed in a given direction is Speed in a given direction is velocityvelocity ( vector).( vector).

What is the velocity of a boat that What is the velocity of a boat that travels from St. John’s, west to Longpondtravels from St. John’s, west to Longpond

(16 Km ) in 2.5 h ?(16 Km ) in 2.5 h ?

AnswerAnswer

Velocity = displacement ÷ Velocity = displacement ÷ timetime

Velocity = 16 Km ÷ 2.5 hVelocity = 16 Km ÷ 2.5 h Velocity = 6.4 km/hVelocity = 6.4 km/h Velocity = 6.4 km/h westVelocity = 6.4 km/h west

Change your answer to m/s!Change your answer to m/s!

= = 6.4 km/h 6.4 km/h ÷ 3.6 = 1.8 m/s÷ 3.6 = 1.8 m/s

Km/hr to m/s conversion trick

Km/hr m/s

m/s K/hr

Divide by 3.6

multiply by 3.6

Difference Between Speed and VelocityScalar

Quantities

( Number and unit)

Volume liters

Distance

Voltage

Speed (KM/h)

Vector Quantities

( Number, unit and direction)

10 Km West

50 Km/hr south

100 newtons right

Velocity (Speed and Direction)

Velocity is a Vector Quantity

Speed is a Scalar

Quantity

Distance-time graphsDistance-time graphs

On your paper, graph the following:On your paper, graph the following: D (m)D (m) T (sec) T (sec)

00 00 55 77 1010 14 14 1515 21 21

Was your graph a straight Was your graph a straight line?line?

A A distance-time graphdistance-time graph which is which is a a straight linestraight line indicates indicates constant speedconstant speed..

In constant speed, the object In constant speed, the object does not speed up or slow does not speed up or slow down. The acceleration is zero.down. The acceleration is zero.

The Steeper the slope the faster the object is moving.

y2

y1

x1 x2

On a distance time graph for uniform motion the slope equals the average speed.

Vavg = Δd Δt

What is the Vavg for this graph?

8 - 4 = 4 = 2m/s4 – 2 2

Displacement Time GraphsDisplacement Time Graphs Like distance time graphs only Like distance time graphs only

displacement can be either positive or displacement can be either positive or negative, therefore we need two negative, therefore we need two quadrants. quadrants.

d d d dt t t t

Moving left awayfrom origin

Moving right towardorigin from left

Stopped right of origin

Stopped left of origin

Graphing Graphing !!

d

t

A

B

C

A … Starts at home (origin) and goes right (+) slowly

B … Stopped (position remains constant as time progresses)

C … Turns around and goes in the (-) direction

quickly, passing by home

Explain what is happening for each leg of the trip.

Explain what is happening for each leg of the trip.

What is the velocity for each leg of the trip?

Hint: slope= rise/ run = Δ d = d2 – d1 = Avg. velocity

t t2 – t1

Graph the following on a Graph the following on a distance-time graph:distance-time graph:

d (m)d (m) t (s)t (s) 00 00 55 11 2020 224545 338080 44125125 55

0 1 2 3 4 5

Was your graph a curve?Was your graph a curve?

A graph that A graph that curvescurves on a on a distance-time graphdistance-time graph shows shows that the object is that the object is accelerating ( non-uniform accelerating ( non-uniform motion).motion).

Acceleration.Acceleration.

Distance-time graphsDistance-time graphs Describe the motion of the object as shown Describe the motion of the object as shown

in the in the graph.graph.

From 0-8 sec, constant speed:(25 m/sec);From 8-12 sec, no motion (stop);From 12-16 sec, acceleration;From 16-20 sec, constant speed

Speed-time graphsSpeed-time graphs

Using the distance-time graph from Using the distance-time graph from the last frame, draw a speed time the last frame, draw a speed time graph. First fill in the table below:graph. First fill in the table below:

Average Speed (m/s)Average Speed (m/s) Time (sec) Time (sec)

________ 0 to 80 to 8

________ 8 to 128 to 12

________ 12 to 2012 to 20

25

0

37.5

Draw on board

What does your graph look What does your graph look like?like?

Constant speedConstant speed will be a will be a horizontal horizontal line on a speed time line on a speed time graph. graph.

If the speed If the speed decreasesdecreases, the line , the line will slant will slant downdown..

If the speed If the speed increasesincreases, the line , the line will slant will slant upup..

On a velocity - time graph the area between the graphed line and the x-axis equals the displacement

Area = l x w = 6 s x 30 m/s = 180 m

This object is slowing down in a positive direction. It is non-uniform motion. However we can still calculate the displacement by finding the area of the triangle. ( ½ base x height )

Displacement = ½ base x height = ½ 25.0 m/s x 25.0

s = 312.5 mNote how the units cancel.

Displacement = area of rectangle + area of a triangle = l x w + ½ base x height = 10.0 s x 5.0m/s + ½ 10.0 m/s x 5.0 s = 50 m + 25 m

= 75m

Object is moving at a constant speed for 5.0 sthen it speeds up for the next 5.0 sec.

Object moving right and speeding up. (+)

Object moving left and speeding up. (-)

Object moving right and slowing down. (+)

Object moving left and slowing down (-)

The slope of the line on a velocity time graph equals the average acceleration.

For uniform motion the graph is horizontal, therefore the slope is zero and the acceleration is zero.

Graphing w/ Graphing w/ AccelerationAcceleration

d

A … Start from rest south of home; increase speed gradually

B … Pass home; gradually slow to a stop (still moving north)

C … Turn around; gradually speed back up again heading south

D … Continue heading south; gradually slow to a stop near the starting point

t

A

B C

D

Tangent Tangent LinesLines

t

SLOPE VELOCITY

Positive Positive

Negative Negative

Zero Zero

d

On a position vs. time graph:

The slope of a tangent line will give the velocity at that point in time. ( instantaneous velocity )

Graphing TipsGraphing TipsThe same rules apply in making an acceleration graph from a velocity graph. Just graph the slopes! Note: a positive constant slope in blue means a positive constant green segment. The steeper the blue slope, the farther the green segment is from the time axis.

a

t

v

t

Area under a velocity graphArea under a velocity graphd

t

“forward area”

“backward area”

Area above the time axis = forward (positive) displacement.

Area below the time axis = backward (negative) displacement.

Net area (above - below) = net displacement.

Total area (above + below) = total distance traveled.

All 3 All 3 GraphsGraphs

t

d

v

t

a

t

What do the following speed-What do the following speed-time graphs depict?time graphs depict?

AccelerationAcceleration

Change in velocityChange in velocity Can be change in speed Can be change in speed oror direction direction

Acceleration = ∆V/ ∆TAcceleration = ∆V/ ∆T

∆ ∆VV aa tt

Acceleration problemAcceleration problem

A roller coaster’s A roller coaster’s velocity at the top velocity at the top of a hill is 10m/s. of a hill is 10m/s. Two seconds later it Two seconds later it reaches the bottom reaches the bottom of the hill with a of the hill with a velocity of 26m/s. velocity of 26m/s. What is the What is the acceleration of the acceleration of the roller coaster?roller coaster?

AnswerAnswer

Acceleration = ∆V/ ∆TAcceleration = ∆V/ ∆T a = a = 26m/s – 10m/s26m/s – 10m/s

2 s2 sa = a = 16m/s16m/s

2s2sa = 8m/s/s or 8m/sa = 8m/s/s or 8m/s22

More acceleration problemsMore acceleration problems

1. A car accelerates at a rate of 1. A car accelerates at a rate of 20Km/hr/s. How long does it take to 20Km/hr/s. How long does it take to reach a speed of 80 Km/hr?reach a speed of 80 Km/hr?

2. A car travels at 60 Kilometers per 2. A car travels at 60 Kilometers per hour around a curve. Is the car hour around a curve. Is the car accelerating?accelerating?

3. A car travels in a straight line at 60 3. A car travels in a straight line at 60 Km/hr. Is the car accelerating?Km/hr. Is the car accelerating?

Answers:Answers:

1. 1. ∆V ∆V 80Km/hr80Km/hr

a ta t 20Km/hr/ t20Km/hr/ t

4sec = t4sec = t

2. yes! Because it’s changing direction!2. yes! Because it’s changing direction!

3. no! It’s not changing speed or 3. no! It’s not changing speed or direction!direction!

DecelerationDeceleration

Negative accelerationNegative acceleration Example: A car slows from Example: A car slows from

60Km/hr to 20 km/hr in 4 60Km/hr to 20 km/hr in 4 seconds. What is its seconds. What is its acceleration?acceleration?

Answer:Answer:

Acceleration = ∆V/ ∆TAcceleration = ∆V/ ∆T Acceleration = Acceleration = Vf – ViVf – Vi

tt a = a = 20km/hr – 60km/hr20km/hr – 60km/hr

4 s4 sa = a = -40Km/hr-40Km/hr

4s4sa = -10Km/hr/sa = -10Km/hr/s

Velocity & Acceleration Sign Velocity & Acceleration Sign ChartChart

V E L O C I T Y ACCELERATION

+ -

+ Moving forward;

Speeding up

Moving backward;

Slowing down

-

Moving forward;

Slowing down

Moving backward;

Speeding up

Acceleration due to Acceleration due to GravityGravity

9.8 m/s2

Near the surface of the Earth, all objects accelerate at the same rate (ignoring air resistance).

aa = - = -gg = -9.8 m/s = -9.8 m/s22

Interpretation: Velocity decreases by 9.8 m/s each second, meaning velocity is becoming less positive or more negative. Less positive means slowing down while going up. More negative means speeding up while going down.

This acceleration vector is the same on the way up, at the top, and on the way down!

Motion Graphs – Position vs. Motion Graphs – Position vs. TimeTime

constant, rightward (+) velocity of +10 m/s

a rightward (+), changing velocity - that is, a car that is moving rightward but speeding up or accelerating

Motion Graphs – Velocity vs. Motion Graphs – Velocity vs. TimeTime

constant, rightward (+) velocity of +10 m/s

a rightward (+), changing velocity - that is, a car that is moving rightward but speeding up or accelerating

Review: Distance-time graph of Review: Distance-time graph of accelerationacceleration

Distance-time graph of Distance-time graph of decelerationdeceleration

Review:Speed-time graph of Review:Speed-time graph of accelerationacceleration

Review: Speed-time graph of Review: Speed-time graph of decelerationdeceleration

Review: Distance-time graph of Review: Distance-time graph of constant speedconstant speed