UNIT 1Motion Graphs

LyzinskiPhysics

x

t

Days 1 - 2

The purpose of this chapter is to learn the 1st step of Mechanics (the study of motion) which is KINEMATICS (the study of

motion with no regards to what is causing the motion). The study

of what is “causing” the motion is known as dynamics, and we will

study this in a later chapter.

- MechanicsKINEMATICS

DYNAMICS- Electricity

- Magnetism

- Optics

- Waves

PHYSICSA “description” of motion

A study of what “causes” motion

Day #1

* Distance * Speed * Scalars * d-t graphs

Definition• Distance (d) – the length of the path

followed by an object

* If an object’s path is straight, the distance is the length of

the straight line between start and finish.

** If an object’s path is NOT straight, the distance is the

length of the path if you were to “straighten it out” and

measure it the way you would measure the length of a

curved shoelace.

start

finish

start

finish

Using the number line above, what would be the distance travelled if an object travelled from …..

- A to B

- A to C

- A to C and then back to A

- C to B, passing through A

B C

-3 -2 -1 0 1

Ameters

1m

4m

4m + 4m = 8m

4m + 1m = 5m

5 yd12 yd

A

B

C

Sally and Timmy are at point A.Sally walks directly to point C (taking the shortest path). Timmy also takes a “shortest path”, but has to stop at point B for lunch first.

How much further has Timmy walked when he arrives?

4 yd

Definition• Average Speed (s) – the distance travelled

during a time interval divided by the elapsed time.

s = d/t

(or s=d/t) Since t = t2 – t1, if t1 = 0, then t = t2 – 0 = t2 = t

Larry walks from point B to point C, and then goes directly to point A. If he walks at an average speed of 6 mph, how long does the trip take him?

B C

-3 -2 -1 0 1

Amiles

d = 3mi + 4mi = 7mis = 6 mi/h

s = d/t t = d/s = (7mi)/(6mi/h)=1.17h

1 h, 10 minUse appropriate units

Larry runs from point A to point B in 5 minutes and then proceeds to jog directly to point C, taking his time in 30 additional minutes. Find…

B C

-3 -2 -1 0 1

Akm

a) Larry’s average speed during the first portion of the trip.

b) The average speed during the second portion of the trip.

c) Larry’s average speed for the entire trip.

s = d/t = (1km)/(5min) = 0.2 km/min = 12 km/h

s = d/t = (3km)/(30min) = 0.1 km/min = 6 km/h

s = d/t = (4km)/(35min) = 0.114 km/min = 6.86 km/h

Definition• Scalar – a quantity that has a magnitude

only, no direction.

* YES, scalars can have units.

** What scalars have we learned about thus far?

___________ ____________ ___________distance speed time

I thought time could march backward?

d-t graphsConstant speed

Speeding UP

Constant Speed (faster!)

Slowing Down

At rest

t (sec)

d (m)

BC

E

A

D

F

10 15 20 27 36

120

100

50

30

Speed on a d-t graph can be found by taking the _______________.SLOPE

sAB = rise/run = (30-0m) / (10-0s) = 3 m/s

sCD = rise/run = (100-50m) / (20-15s) = 10 m/s

t (sec)

d (m)

BC

E

A

D

F

10 15 20 27 36

120

100

50

30

Open to in your Unit 1 packet

520 – 170yd = 350 yd (approximately)

1) On the d-t graph, find the distance travelled from 4 to 16 seconds. ______

1

d-t graphs CANNOT have sharp points

NOTHING CAN STOP INSTANTANEOUSLY!!

Day #2

* Position* Displacement * Average Velocity* Vectors* x-t graphs

Definition• Position (x) – the location of an object with

respect to a specified reference point.

*We choose this reference point to be the origin of a

coordinate system.

-3 -2 -1 0 1

Akm

6 7 8 9 10

The position of particle “A” is either x = -3 or x = 6, depending on which reference point (or origin) you use.

Definition• Displacement (x) – the change in an

object’s position during a time interval.

x = x2 – x1or

x = xf – xi

*Displacement must have both a magnitude (size) and a

direction (right, left, up, down, north, south, etc).

These are all VECTORS.

What’s a vector?

Using the number line above, find the distance travelled and the displacement in moving from

- A to B

- C to A

- A to C and then back to A

- C to B, passing through A

B C

-3 -2 -1 0 1

Ameters

1m, 1m [right]

4m, 4m [left]

8m, 0m

4m, 3m [left]

x = 1 – (1m) = 0m

x = (-2) – (1m) = -3m OR 3m [left]

Definition• Average Velocity ( v ) – the displacement

of an object divided by the elapsed time.

v = x/t

(or v=x/t)

A D

B C

Sam runs the 400m dash. He starts and finishes at point A, travelling one complete circuit around the track. Each section of the track is 100m long. His average speed during each interval are as follows.

AB: 7 m/sBC: 8 m/sCD: 6 m/s

DA: 7.5 m/s

s = d/t t = d/s = 100m/7sec = 14.286 sec100m/8sec = 12.5 sec100m/6sec = 16.667 sec100m/7.5sec = 13.333 sec

s = d/t = (400m)/(56.786s) = 7.04 m/sec

Find Sam’s avg. speed and avg. velocity for the entire trip.

Avg Velocity = 0 since x = 0 for the entire trip.

A D

B C

Sam runs the 400m dash. He starts and finishes at point A, travelling one complete circuit around the track. Each section of the track is 100m long. His average speeds during each interval are as follows.

AB: 7 m/s, 14.286 secBC: 8 m/s, 12.5 sec

CD: 6 m/s, 16.667 secDA: 7.5 m/s, 13.333 sec

31.831 m

100

104.94

Find Sam’s average speed and average velocity for the 1st half of the race.

s = d/t t = d/s = 200m/(14.286+12.5s) = 7.47 m/s

v = x/t = (104.94m )/(14.286+12.5s) = 3.92 m/sec

Definition• Vector – a quantity that has both magnitude

AND a direction … oh yeh!

* YES, vectors can have units.

** What vectors have we learned about thus far?

____________ ________________ ___________position displacement velocity

Scalars vs. Vectors

has magnitude & direction (example: 15 cm east)

has a magnitude only (example: 6 ft)

1 2

AB

Displacement is NEVER greater than distance traveled!

Displacement:

Distance:

Scalars vs. Vectors (continued)

has magnitude & direction (example: 15 mi/h North)

has a magnitude only (example: 30 km/h)

If an object STARTS & STOPS at the same point, the velocity is ZERO! (since the displacement is zero)

Velocity:

Speed:

1

2

24 km

7 km

Total time for the trip from 1 to 2: 1 hr

Speed = 31 km/h

Velocity = 25 km/h at 16o NE

25 km

16o Don’t worry about this notation for this test

x-t graphs

t (sec)

x (m)

t1 t2 t3

x2

x1

x3

B

C

D

A

Constant speed (Constant + velocity, or constant velocity in the + direction)

Slow down, speed up, slow down, speed up

2 moments where the object is “at rest” (for a moment)

How to get the position (x) at a certain time (t) off an x-t graph

x(m)

10 20 30 40 50

t (s)

30

20

10

0

Example:

What is the position at t = 30 seconds?

Go over to t = 30.

Find the pt on the curve.

Find the x value for this time.

24m

How to calculate the displacement between two times on an x-t graph

x(m)

10 20 30 40 50

t (s)

30

20

10

0

Example:

What is the displacement from t = 10 to t = 40?

Find x1

Find x2

Use x = x2 - x1 = + 7 m 10 m

17 m

How to find the distance traveled between two times on an x-t graph.

x(m)

10 20 30 40 50

t (s)

30

20

10

0

Example:

What is the distance traveled from t = 10 to t = 40?

Find the distance traveled in the + direction.

Find the distance traveled in the - direction.

Add them together. (27 m)

17 m10 m

Understand the difference between velocity and speed on an x-t graph.

x(m)

10 20 30 40 50

t (s)

30

20

10

0

Example:

What is the average speed from t = 10 to t = 40 seconds?

dist10-40 = 27 m

(previous slide)

Avg. Speed = dist/ t

= 27m / 30 sec

= 0.9 m/s

17 m

10 m

Understand the difference between velocity and speed on an x-t graph.

x(m)

10 20 30 40 50

t (s)

30

20

10

0

Example:

What is the average velocity from t = 10 to t = 40 seconds?

Avg. Velocity = slope

= x/ t

= + 7 / 30 sec

= + 0.23 m/s

x10-40 = + 7 m (previous slide)

Will avg. velocity EVER be greater than avg. speed?

NO!!!Will avg. velocity EVER be

equal to avg. speed?

YES!!! When the path travelled was one-way, in

a straight line.

Negative Average Velocity?

x(m)

10 20 30 40 50

t (s)

30

20

10

0

Avg. vel. = slope = rise/run = -7 m / 20

= -.35 m/s

Example:

What is the average velocity from t = 20 to t = 40 seconds?

Since the objects displacement is in the NEGATIVE direction, so is its average velocity.

1) On the x-t graph, find the position at 9 seconds. ______

2) On the x-t graph, find the average speed AND the average velocity from 6 to 12 seconds.

3) On the x-t graph, name all the times (or time intervals) during which the object is at rest.

-10 m

avg velocity = slope = -15m / 6sec = -2.5 m/s s = |v| = 2.5 m/s

At rest at t = 0 and t = 12 sec

Open to in your Unit 1 packet1

2)

3)

4)

1) On the x-t graph, name each different motion interval (hint: there are 7 answers).

2) On the x-t graph, find the displacement during the 1st 21 seconds.

x = x2 – x1 = (-10m) – (10m) = -20m (approximately)

5)

6)

Speeding up, const negative vel, slowing down, speeding up, const positive velocity(slow), speeding up, constant positive velocity (fast)