LINEAR MOTIONLINEAR MOTION

UNIT 2AUNIT 2A

distance | speed | direction acceleration

Unit 2AUnit 2A: : Linear MotionLinear Motion (Chap 2)

You can describe the motion of an object by its:

How do you know if an object is moving?

• Is your book moving?

The book is at rest,relative to the table, BUT

It’s moving at about30 km/s relative to the sun.

2.1 Motion Is Relative

An object is moving if its position relative to a fixed point is changing.

An object’s motion must be described relative to something else.

• shuttle 8 km/s relative to Earth below

• race car 300 km/h relative to the track

• The speeds of things on Earth are usually measured relative to the Earth’s surface.

2.1 Motion Is Relative

Reference point

Motion

Problem:You are a passenger in a car stopped at a stop sign. Out of the corner of your eye, you notice a tree on the side of the road begin to move forward.

You have set yourself as the reference point as the car rolls slightly backward.

WHAT??

400 yrs ago, people described motion as simply “slow” or “fast.”

Galileo was the first to measure speed by the distance covered and the time it takes.

2.2 Speed

speed =

distance

time

avg. speed =

5 mi

0.20 h

avg. speed = 25 mi/h

2.2 Speed

Instantaneous Speed

Cars do not always move at a constant speed.

You can tell the speed of the car at any instant by looking at the car’s speedometer.

instantaneous speed:the speed at any instant

2.2 Speed

average speed: total distance time

If we know average speed and travel time, the distance traveled is easy to find.

ExampleExample: If your average speed is 80 km/h on : If your average speed is 80 km/h on a 4-hour trip, then how far did you travel?a 4-hour trip, then how far did you travel?

distance = distance = 80 km80 km = x km = x km 1 h1 h 4 hr 4 hr

2.2 Speed

speed =

distance

time

distance = speed x time

320 km320 km

If a cheetah can maintain a constant speed of 25 m/s, it will cover 25 meters every second.

At this rate, how far will it travel in 10 seconds?

distance = (25 m) = (x m) = (1 s) 10 s

In 1 minute?

distance = (25 m) x (x m) = (1 s) (60 s)

2.2 Speed

250 m

1500 m

distance = speed x time

The speedometer in every car also has an odometer that records the distance traveled. If the odometer reads zero at the beginning of a trip and 35 km a half hour later,

what is the average speed?

2.2 Speed

speed =

distance

time=

35 km

0.5 h=

70 km/h

1. Jake walks east through a passenger car on a train that moves 10 m/s in the same direction. Jake’s speed relative to the car is 2 m/s. Jake’s speed relative to an observer at rest outside the train is ___.

A. 2 m/s

B. 5 m/s

C. 8 m/s

D. 12 m/s

Quick Quiz!

2.1

2. A gazelle travels 2 km in a half hour. The gazelle’s average speed is ___.

A. 1/2 km/h

B. 1 km/h

C. 2 km/h

D. 4 km/h

Quick Quiz.

2.2

In physics,

Velocity: is speed in a direction.direction.

• speed: 60 km/h

• velocity: 60 km/h north, or right, or down…

2.3 Velocity

v =

∆dt

∆: change in… (final – initial)

(df – di) t

ms

(m/s)

If either the speed or the direction (or both)changes, then the velocity changes.

• constant speed and constant velocity are NOT the same.

2.3 Velocity

The car speedometer always reads 30 km/h.

Is speed constant?

Is velocity constant?

Y

N

We can change an object’s motion by changingits speed, its direction, or both.

Acceleration is the rate at which velocity changes.

2.4 Acceleration

a =

∆vt

(vf – vi) t

acceleration can increase or decrease speed,

We can change an object’s motion by changing its speed, its direction, or both.

Acceleration: is the rate at which velocity changes.

2.4 Acceleration

a =

∆vt

(vf – vi) t

acceleration can increase or decrease speed,deceleration is really negative acceleration (–a)

Acceleration concerns change in velocity so any a change in direction is acceleration.

2.4 Acceleration

The car speedometer always reads 30 km/h.

Is velocity constant?

Is there an acceleration?

N

Y

2.4 Acceleration

a in the same direction as v : speed up

2.4 Acceleration

a in the same direction as v : speed upa in the opp. direction as v : slow down

a in the same direction as v : speed up

2.4 Acceleration

a in the opp. direction as v : slow downa at an angle to v : change direction

v units are in distance per time: (m/s)

• a is the change in v per change in time.

• a units are v per time: (m/s per s) or (m/s2)

• changing v from 0 m/s to 10 m/s in 1 s,a is…

2.4 Acceleration

a =

∆vt

m/ss

m s2

or

a =

10 m/s – 0 m/s 1 s

=

10 m/s1 s

10 m/s2=

In 5 seconds a car increases its speed from 8 m/s to 18 m/s, while a truck goes from rest to 10 m/s in a straight line. Which undergoes greater acceleration?

2.4 Acceleration

acar = 18 m/s – 8 m/s

5 s=

10 m/s5 s

2 m/s2=

atruck = 10 m/s – 0 m/s

5 s=

10 m/s5 s

2 m/s2=

1. Constant speed in a constant direction is…

A. constant velocity.

B. constant acceleration.

C. instantaneous speed.

D.average velocity.

Quick Quiz!

2.3

2. A vehicle undergoes acceleration when it __.

A. gains speed.

B. decreases speed.

C. changes direction.

D. ALL of the above

Quick Quiz.

2.4

Imagine there is no air resistance and that gravity is the only thing affecting a falling object.

• An object moving under influence of the gravitational force only is said to be in free fall.

2.5 Free Fall: How Fast

During each 1 s of fall, v increases by 10 m/s.

This gain in v in m/sis a in m/s2.

2.5 Free Fall: How Fastt = 0 s, v = 0 m/st = 1 s, v = 10 m/s

t = 2 s, v = 20 m/s

t = 3 s, v = 30 m/s

t = 4 s, v = 40 m/s

t = 5 s, v = 50 m/s

g is used for the acceleration due to gravity

Although g varies slightly based on altitude, its average value is nearly 10 m/s2

g = –10 m/s2

v = vi + at (a is g)

An object is thrown straight up:

• It moves upward for a while.

• What is v at its highest point?

• Going up, vi goes to 0 m/s.

• a = ?

• It then falls downward as if it had been dropped from rest,going from 0 m/s back to vi (but downward)

• a = ?

2.5 Free Fall: How Fast

v = 0 m/s at hmax vo a = –10 m/s2 = g

a = –10 m/s2 = g

What would the speedometer reading on the falling rock be 4.5 seconds after it drops from rest? (v = ?)

2.5 Free Fall: How Fast

How about 8 seconds after it is thrown with an initial velocity of 20 m/s downward?

v = vi + atv = 0 m/s + (–10 m/s2)(4.5 s)

v = –45.0 m/s

v = –20 m/s + (–10 m/s2)(8 s)

v = –100 m/s

(a is g)

Drop a feather and a coin and the coin reaches the floor far ahead of the feather. Why?

Air resistance is responsible for these different accelerations. (not just g)

In a vacuum, the feather and coin fall with exactly the same acceleration, g.

2.8 Air Resistance and Falling Objects

With what objects might air resistance be small enough to be ignored?

2.6 Free Fall: How Fart = 0 s, v = 0 m/s, d = 0 m

g = –10 m/s2

v = vi + at

t = 1 s, v = 10 m/s, d = 5 m

t = 2 s, v = 20 m/s, d = 20 m

t = 3 s, v = 30 m/s, d = 45 m

t = 4 s, v = 40 m/s, d = 80 m

t = 5 s, v = 50 m/s, d = 125 m

d = vit + ½at2

d = 35 m

vavg = (30 + 40) 2vavg = 35 m/s

1 s

d = 45 m

vavg = (40 + 50) 2vavg = 45 m/s1 s

(a is g)

An apple falls to the ground in 3 s.

What is its speed upon striking the ground?

2.6 Free Fall: How Far

vf = vi + atv = 0 m/s + (10 m/s2)(3 s)

v = 30 m/s

vavg = (0 m/s + 30 m/s) 2

vavg = 15 m/svavg = (vf + vi) 2

1 s

2 s

3 s

What is its vavg during the 3 s?

(a is g)

An apple falls to the ground in 3 s.

How high above ground was the apple when it first dropped?

2.6 Free Fall: How Far

d = vit + ½at2

v = 30 m/s

vavg = 15 m/s

d = (0 m/s)(3 s) + ½(10 m/s2)(3 s)2

d = 45 m

1 s

2 s

3 s

(a is g)

Linear Motion - Practice Problems

1) An angry mob lynches a physics teacher after receiving their grades. They throw the physics teacher off a tall building straight down with a velocity of 20 m/s. The teacher falls for 3.0 seconds landing on a stack cardboard boxes. From what height was he thrown?

d = vi t + ½ at2

Linear Motion - Practice Problems

2) Find the uniform acceleration that causes a car’s velocity to change from 32m/s to 96m/s in an 8.0s period.

3) A car with a velocity of 22m/s is accelerated uniformly at a rate of 1.6m/s for 6.8s. What is the final velocity?

vf = vi + at

vf = vi + at

Linear Motion - Practice Problems

4) An airplane starts from rest and accelerates at a constant 3.0m/s2 for 30s before leaving the ground. a)How far did it move?b)How fast was it going at liftoff?

d = vi t + ½ at2

vf = vi + at

Linear Motion - Practice Problems

5) Your sister drops your house keys down to you from the second floor window. If you catch them 4.3 m from where your sister dropped them, what is the velocity of the keys when you catch them?

d = vit + 1/2at

1. In a vacuum tube, a feather is seen to fall as fast as a coin. This is because …

A. gravity doesn’t act in a vacuum.

B. air resistance doesn’t act in a vacuum.

C.greater air resistance acts on the coin.

D.gravity is greater in a vacuum.

Quick Quiz!

2.8

2. If a falling object gains 10 m/s each second it falls, its acceleration can be expressed as _________.

A. 10 m/s/s

B. 10 m/s2

C.v = gt

D.both A and B

Quick Quiz.

2.5

3. A rock falls 180 m from a cliff into the ocean. How long is it in free fall?

A. 6 s

B. 10 s

C.18 s

D.180 s

Quick Quiz.

2.6

d = vit + ½at2

180 = (0)t + ½(10)t2

180 = ½(10)t2

180 = 5t2

180 = t2

5

36 = t2

√36 = t t = 6 s

Equations, tables, and pictures are not the only way to describe relationships between distance, velocity, and acceleration.

Graphs can visually describe relationships.

2.7 Graphs of Motion

distance vs. time:

2.7 Graphs of Motiond

ista

nce

(m

)

time (s)

slope = distance = v time

constant velocity (a = 0)

distance vs. time:

2.7 Graphs of Motiond

ista

nce

(m

)

time (s)

slope = distance = v time

parabolic curve b/c time is squared(quadratic)

d = ½at2

constant acceleration (+a)

2.7 Graphs of Motiond

t

d

t

d

t

distance vs. time

dir:v :

a :

1

3

2 →+

fast

0

dir:v :

a :

→+

slow

0

dir:v :

a :

←–

slow

0

dir:v :

a :

←–

fast

0

4d

t

2.7 Graphs of Motiond

ista

nce

(m

)

time (s)

Describe the motion.

v : +

a : 0

v : 0

a : 0

• moves forward at v = 5 m/s for 5 s.• stops at 25 m (v = 0 m/s) for 5 s.

velocity vs. time: constant velocity (a = 0)2.7 Graphs of Motion

velo

city

(m

/s)

time (s)

slope = velocity = a time

velocity vs. time: constant acceleration (+a)2.7 Graphs of Motion

velo

city

(m

/s)

time (s)

slope = velocity = a time

2.7 Graphs of Motion

dir: v : a :

right+ (constant) 0

dir: v : a :

left– (constant) 0

dir: v : a :

right+ (faster) +

dir: v : a :

left– (slower) +

right+ (slower) –

dir: v : a :

left– (faster) –

dir: v : a :

2.7 Graphs of Motion

tv

+

–

0

Consider the graph below. Describe the motion.(include all that are true):

A.moving forward

B.constant velocity

C.positive velocity

D.negative velocity

E.slowing down

F.changing directions

G.speeding up

H.positive acceleration

I.constant acceleration

J.negative acceleration

The slope of a velocity-versus-time graph represents ____.

A. distance

B. velocity

C. acceleration

D. time

Quick Quiz!

Consider the graph below. Describe the motion from...

A. t = 0-1 s B. t = 1-4 s C. t = 4-9 s D. t = 9-12 s v =

a =

→, faster

+

+ v =

a =

→, faster

v =

a =

→, slower

+

+

+

– v =

a =

←, faster

–

–

WARM UPWARM UP

At what time

is v = 0 m/sv = 0 m/s at 9 s

Equations Summary

speed =

distance

time

v =

∆d

t

a =

∆v

t

v = vi + at vavg = (vf + vi)

2

d = vit + ½at2 g = –10 m/s2

NOT

given on test

given on test

NN

WS Motion Graphs

Begin your worksheet now.

We will take all of class tomorrow to finish it.

2.7 Graphs of Motiond

t

d

t

d

t

distance vs. time

1

3

2dir:v :

a :

____

_____

__

dir:v :

a :

____

____

__

dir:v :

a :

____

_____

__

d

t

dir:v :

a :

____

_____

__

4

_______ (______) __

2.7 Graphs of Motion

dir: v : a :

_______ (______) __

dir: v : a :

_______ (______) __

_______ (______)

__

dir: v : a :

dir: v : a :

_______ (______) __

_______ (______)

__

dir: v : a :

dir: v : a :

velocity vs. time

https://www.youtube.com/watch?v=rD0tmgMdbQg

VIDEO – Part 1(7:19)

Acceleration & Velocity Acceleration & Velocity GraphsGraphs

https://www.youtube.com/watch?v=JFZ2W5PwlrY

VIDEO – Part 2(9:53)

Acceleration & Velocity Acceleration & Velocity GraphsGraphs

https://www.youtube.com/watch?v=nPhRrhb99rY

VIDEO – Part 3(7:45)

Acceleration & Velocity Acceleration & Velocity GraphsGraphs