Post on 26-Mar-2015
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