Ch. 11Ch. 11MotionMotion

Describing Motion Motion Speed & Velocity Acceleration

A. MotionA. Motion

MotionChange in position in relation to

a reference point.

Reference point

Motion

A. MotionA. Motion

Problem: How fast is the bumblebee flying?

We need a frame of reference... nonmoving point from which motion

is measured. What could be used as a frame of

reference in the illustration above?

Example:1. Describe the motion of the fish in the cat’s frame of reference.2. Describe the motion of the cat in the fish’s frame of reference.

3. Which one is “really” moving; the cat or the fish?

RELATIVE MOTION:Movement in relation to a frame

of reference.EX: Passengers on a rollercoaster appear to onlookers on the ground to be speeding by

Yet, when the people on the roller coaster look at each other, they don’t appear to be moving at all

A. MotionA. Motion

Consider the following scenario: 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 mistakenly set yourself as the reference point.

Choosing a meaningful frame of reference is important in clearly describing motion!

A. MotionA. Motion

DistanceLength of a pathChoose a unit with

appropriate size SI unit: meter (m) Long distances = km Short lengths = cm, mm

A. MotionA. Motion

DisplacementDistance and direction from

starting point The Millenium Force

roller coaster travels 6,595 ft throughout the ride (distance)

It’s total displacement is zero!

A. MotionA. Motion

VectorHas magnitude (size, length,

amount) and direction.Shown as an arrow pointing in an

appropriate direction (up, down, N, S, etc); length shows magnitude

Vector

A. MotionA. Motion

Example 1:

A fire truck drives 10 miles East, then turns around and drives 2 miles West.

Displacement = 10 miles E

Displacement = 2 miles WSum Vector/Disp. = 8 miles E

A. MotionA. Motion

Example 2:

The school bus travels 2 miles East, then stops to pick up students, and continues to travel an additional 3 miles East.

2 miles E 3 miles E

Resultant Vector/ Total Disp. = 5 miles E

B. Speed & VelocityB. Speed & Velocity

Speed rate of motion distance traveled per unit time

time

distancespeed

vd

t

B. Speed & VelocityB. Speed & Velocity

Instantaneous Speedspeed at a given instant

Average Speed

time total

distance totalspeed avg.

B. Speed & VelocityB. Speed & Velocity

Problem: You are driving down Olio road, look

at your speedometer, and realize you’re going 80 mph. A cop clocks you. Has he measured your average or instantaneous speed?

Instantaneous! You weren’t driving 80 mph the entire trip!

B. Speed & VelocityB. Speed & Velocity

Problem: Your family is driving to Florida for a

vacation. The trip is 1200 miles long and it takes 20 hours to get there. Is 60 mph your instantaneous speed?

No! You probably sped up, slowed down, stopped for gas, or stopped to eat at several instances during the trip.

B. Speed & VelocityB. Speed & Velocity

Problem:A storm is 10 km away and is

moving at a speed of 60 km/h. Should you be worried?

It depends on the storm’s direction!

B. Speed & VelocityB. Speed & Velocity

Velocityspeed in a given directioncan change even when the

speed is constant!

C. CalculationsC. Calculations

1) Your neighbor skates at a speed of 4 m/s. You can skate 100 m in 20 s. Who skates faster?

GIVEN:

d = 100 m

t = 20 s

v = ?

WORK:

v = d ÷ t

v = (100 m) ÷ (20 s)

v = 5 m/s

You skate faster!vd

t

C. CalculationsC. Calculations

2) Sound travels 330 m/s. If a lightning bolt strikes the ground 1 km away from you, how long will it take for you to hear it?

GIVEN:

v = 330 m/s

d = 1km = 1000m

t = ?

WORK:

t = d ÷ v

t = (1000 m) ÷ (330 m/s)

t = 3.03 s

vd

t

C. CalculationsC. Calculations

3) The slowest animal ever discovered traveled with a speed of 5.7 km/y. How far would the crab travel in 15 y?

GIVEN:

v = 5.7 km/y

t = 15 y

d = ?

WORK:

d = v x t

d = (5.7 km/y) x (15 y)

d = 85.5 km

vd

t

C. CalculationsC. Calculations

4) What is the speed of the Mediterranean crab from problem #3 in meters per day?

GIVEN:

v = 5.7 km/y

= ? m/day

WORK:

5.7 km/y x (1 mi/1.6 km) x (1 y/365 days) =

d = .0098 mi/day

D. AccelerationD. Acceleration

Acceleration the rate of change of velocitychange in speed or direction

t

vva if

a: acceleration

vf: final velocity

vi: initial velocity

t: time

a

vf - vi

t

D. AccelerationD. Acceleration

Positive acceleration “speeding up”

Negative acceleration “slowing down”

D. CalculationsD. Calculations1) A roller coaster starts down a hill at 10 m/s.

Three seconds later, its speed is 32 m/s. What is the roller coaster’s acceleration?

GIVEN:

vi = 10 m/s

t = 3 s

vf = 32 m/s

a = ?

WORK:

a = (vf - vi) ÷ t

a = (32m/s - 10m/s) ÷ (3s)

a = 22 m/s ÷ 3 s

a = 7.3 m/s2a

vf - vi

t

D. CalculationsD. Calculations

2) How long will it take a car traveling 30 m/s to come to a stop if its acceleration is -3 m/s2?

GIVEN:

t = ?

vi = 30 m/s

vf = 0 m/s

a = -3 m/s2

WORK:

t = (vf - vi) ÷ a

t = (0m/s-30m/s)÷(-3m/s2)

t = -30 m/s ÷ -3m/s2

t = 10 sa

vf - vi

t

E. Graphing MotionE. Graphing Motion

slope =

steeper slope =

straight line =

flat line =

Distance-Time Graph

A

B

faster speed

constant speed

no motion

speed

E. Graphing MotionE. Graphing Motion

Who started out faster? A (steeper slope)

Who had a constant speed? A

Describe B from 10-20 min. B stopped moving

Find their average speeds. A = (2400m) ÷ (30min)

A = 80 m/min B = (1200m) ÷ (30min)

B = 40 m/min

Distance-Time Graph

A

B

0

100

200

300

400

0 5 10 15 20

Time (s)

Dis

tan

ce (

m)

Distance-Time Graph

E. Graphing MotionE. Graphing Motion

Acceleration is indicated by a curve on a Distance-Time graph.

Changing slope = changing velocity

E. Graphing MotionE. Graphing Motion

0

1

2

3

0 2 4 6 8 10

Time (s)

Sp

ee

d (

m/s

)

Speed-Time Graph

slope =

straight line =

flat line =

acceleration +ve = speeds up -ve = slows down

constant accel.

no accel. (constant velocity)

E. Graphing MotionE. Graphing Motion

0

1

2

3

0 2 4 6 8 10

Time (s)

Sp

ee

d (

m/s

)

Speed-Time GraphSpecify the time period

when the object was... slowing down

5 to 10 seconds speeding up

0 to 3 seconds

moving at a constant speed 3 to 5 seconds

not moving 0 & 10 seconds