aphical Analysis of motion in ______________ Distance and displacement. What is the total distance moved? hat is the resultant displacement? 20 + 10 = 30 m +10 m d (m) t (s) 20 10 5 10 15 one direction d the average speed in the 0-5 s interval. eat for 5-10 s and 10-15 s. 20 m 5 s 0 m , 5 s 10 m 5 s
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Graphical Analysis of motion in _________________ I.Distance and displacement. What is the total distance moved? What is the resultant displacement? 20.
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Graphical Analysis of motion in _________________
I. Distance and displacement.
What is the total distance moved?What is the resultant displacement?
20 + 10 = 30 m
+10 m
d (m)
t (s)
20
10
5 10 15
one direction
Find the average speed in the 0-5 s interval.
Repeat for 5-10 s and 10-15 s.
20 m5 s
0 m ,5 s
10 m5 s
II. Uniform motion – ____________ is constant
d
t
slope =_____
A
B
= ________
slope =______________
speed = _______________
Slower less slope
A. Graph of d vs. t
What would the graph of a slower object look like?
________d in each _____
How much slower is B?1 2
velocity
d/t speed v
constant
constantsame t
half the speed of A
v
t
A
B
B. Graph of speed __________ for uniform motion
slope =______
aslope =________________
a =_________
B is slower lower
What does the area shown represent?
area = L x W = _____________ =_____________
units: ______ x ______ = _________
What about B?
v vs. t
v/t
slope =______constant = 0
0
speed x time distance
[m/s] [s] [m]
a
t
C. Graph of a vs. t for uniform motion
In review: for __________________ Motion:
d
t
A
B
t
v AB
a
t
a = 0
Same.
a = 0
How would you graph B?
Uniform
paper
tape constant v
timer marks the tape at constant ________ intervals
As car moves, describe pattern of marks on tape.
Ex: tape timers
_____________ spaced b/c car moves the __________ d between each mark.
timer
cart pulls tape________________
time
through timer
How would tape look if car was twice as fast?
Equallysame
III. Non-uniform motion: ___________________ acceleration
d
t
slope of tangent is the______________________
The slope ___________
b/c speed v ___________
A. Graph of d vs. t for object beginning at rest
0
1
2
Object covers ________ din each________________
dashed linesare__________
constant (non-0)
t interval
more
increases
increases
instantaneous v
tangents
________speed vi = ___ __________________
initial 0slope = 0 at t = 0
v
t
B. Graph of speed v vs. t for __________________acceleration a beginning _______________ .
slope =________
= __________
slope = _______________
a = ______________
What does the area shown represent?
area = (1/2) bh = (½) ______________=__________
units: ______ x ______ = ______
constant (non-0)at rest
v/t
accel. a
constant ≠ 0
constant
time x speed distance
[s] [m/s] [m]
a
t
C. Graph of a vs. t for constant a
a = constant
In review: For _________________________acceleration
d
t
v
t
a
t
constant, non-zero
cartpaper
tapeconstant a
As car moves, describe pattern of marks on tape.
Ex:
_______________ spaced b/c car moves _________distance d between each mark.
Timer tape for ___________________
Un-equally
How would tape look if car had more acceleration?
more
constant a
timer
Compare ____________ to ________________motion:
d
t t
v a
t
d
t
v
t
a
t
Uniform
Accel.
slope = v slope = a
area = d
area = d
uniform accelerated
Ex. Answer the questions based on the graph atright.
d (m)
4
2 4 6t (s)
-8
What is the total distance traveled?
What is the resultant displacement?
8 + 8 + 4 = 20 m
+4 m
Find the average speed in the first 2 s.
Find the average speed over the entire 6 s.
Find the average velocity over the entire 6 s.
0
8 m2 s
20 m6 s
+4 m6 s
Ex: The graph below describes a UFO moving in a straight line.
A B
C
Find vavg, d, and a in regions A, B and C.
t (s)
v(m/s)
4.0 8.0 12
20.
40.
In A: v = vi + vf
2
= 30. m/s
v = d/t
d = v t = (30. m/s)(4.0 s)
= 120 m
= area in A
a = Δv/t
= (vf – vi)/t
= (20. m/s + 40. m/s) / 2
= (40. m/s – 20. m/s) / 4.0 s
= 5.0 m/s/ s = 5.0 m/s2
In B: v = vi + vf
2
= 40. m/s
v = d/t
d = v t = (40. m/s)(6.0 s)
= 240 m
= area in B
a = Δv/t
= (vf – vi)/t
= (40. + 40.) / 2
= (40. m/s – 40. m/s) / 6.0 s
= 0
In C: v =
= 20. m/s
d = v t = (20. m/s)(2.0 s)
= 40. m
= area in ΔC: ½bh
a = Δv/t
= (vf – vi)/t
(40. + 0) / 2
= (0 m/s – 40. m/s) / 2.0 s
= -20. m/s2
= v
240 m
t (s)4.0 8.0 12
v(m/s)
20.
40.
A B
C
area = d
a= slope
Which area, A, B or C, is uniform motion?
Which area, A, B or C, is the accelerationconstant, but not zero?