AcceRerationlFree FaaU
I
Name
ÿ ÿ ÿ.ÿ
/
Physics
Acceleration/Free Fall
Test Date:
, :L-I
"Nothing happens until something moves."
-Albert Einstein
AccelerationlFree Fa[H
015 ÿlq Cÿ/ÿCÿIis a change of position in a certain direction, not the total distance traveled
Dimensional Moti:on
[] The simplest kind of motion
[] Things can move forward and backward, but not
[] This also includes " (9 ÿ " and" C)()tas
"for Free Fall
Displacement
[] When [hings start moving, the
I gl'ÿl cÿ\
of a straight line drawn from the object's
position is it's displacement
position to it's
[] In one dimension... Think trains...
Change in position along x-axis = (final position on x-axis) - (initial position on x-axis)
Motion in One Dimension
[] Same concepts apply to any axis!
- Space shuttles instead of trains
/
Change in position along y-axis
Ay - Ys -- Yi
\
= (final position on y-axis) - (initial position on y-axis)
AccelerationlFree Fall
THE Equations
m xf
Ax m
Vi "ÿVf
V avg --
Xi
Ax
2
1
AN -- 7 (vi -Jr V f )lÿt
At
vf
-- Vi Jr- aAt
1
Ax - viAt +- a(At)2
2
,
i¸
!
dÿ
POSITIVE AND NEGATIVE QUANTITIES ARE JUST
¢ o Cÿ 0 kÿc IN MOTION PROBLEMS
AccNerationiFree FalH
Average Velocity
[] Average velocity is the total )0/Q($-fÿcÿI divided by the-]/'ÿq C
interval during which the displacenÿent occurred.
V
aÿ
=
Ax
At
X+ =
Average velocity =
Velocity and Speed
describes motionwith both a ÿig"C C-ÿiOl"x
t l
%/%
(a magnitude)]
([] ,-DD-C. £..J
V
has no direction, only magnitude.
[] Average speed is equal to the total distance traveled divided by the time interval.
I
Fill in the formulas for velocity and speed here:
C+ta+ £ ++
T;,+,e l:,J <,"+r>,+, i'
$p++d -ÿ.
oÿ r f 7-c, ÿ c< ÿv> tie {ÿJ
!-, >.,. +f t-;:-<,,ÿ,.ct.
AccelerationlFree FaJa
[] You're in your car, driving at 100 km/h
- Situation 1' see a red light a quarter-mile away, so you slow down to a stop
- Situation 2: a deer runs out in front of you, so you slam on your brakes to stop
[] In which situation do you feel the most?
5; t ,, cÿ;!, c,,ÿ "L
[] In both cases velocity: Cÿ,caÿ,ÿ(ÿ
(]ÿ.4;ÿ.,.ÿ,, 1.0,ÿ1 kÿ.',",ÿ
Acceleration is:
® "rate of ÿ(ÿ of velocity with respect to time"
• Acceleration is a vector quantity
aavg --
Av VC ÿ vi
,st = )
Average acceleration =
°
With an average acceleration of- 1.2 rn/s2, how long will it take a cyclist to bring a bicycle with an initial
speed of 6.5 rn/s to a complete stop?
OÿC,z .... /,')_ T o c, ÿ-: -i,)_-r q-ÿd, iÿt
,
Suppose a treadmill has an average acceleration of 4.7 x 10.3 m/s2.
a. How much does its speed change after 5.0 min?
o;tÿ .-ÿ U.r,
{t,7 %l.O ÿ 'f. ÿ o os :ÿ ,
b. If the treadmill's initial speed is 1.7 m/s, what will its final speed be?
)
i
\
'
( ) ÿ.1 lll.)'ÿ J t,,,,,' ' ,ÿ ,i! ÿ,,
/
/
/
AccelerationlFree Falm
Graphs can tell us things:
B
s ....... s ........
Time
Figure 1 0
When the velocity in the positive
direction is increasing, the acceleration is positive, as at point A. When
the velocity is constant, there is no
acceleration, as at point B.When
the velocity in the positive direction
is decreasing, the acceleration is
negative, as at point C.
Small Group Questions
[] If a baseball has zero velocity at some instant, is the acceleration of the baseball necessarily zero at that
instant? ÿ'ÿ () ,,
-;A-, r0
()ÿCC/<ÿv c,ÿ-iOÿ
ÿx,s- -t t,4 pcÿ,
COt. tO)
ÿ-?r
t-ÿav fL tÿadC [/C[0(;4ÿ3
¢c,f L4- t,<ÿ,,ÿd ÿ J-.; ÿ! bc
[] If a passenger train is traveling on a straight track with a negative velocity and a positive acceleration, is
it speeding up or slowing down?
C.Mÿ.
'=
[] When you are out for a bike ride, you slow down on your bike as you approach a group of hikers on a
trail. Explain how your acceleration can be positive even though your speed is decreasing.
Acce[eratienlFree Fail
Table 3
Velecilty a.d Ac©e|eratien
vI
a
Motion
+
+
speeding up
-
-
speeding tip
+
-
slowing down
-
+
slowing down
-or+
0
constant velocity
0
-or+
speeding up from rest
0
remaining at rest
FREE FALL
.
For all objects in free-fall (under the effects of the force of gravity only) near the surface of the earth, the
acceleration due to gravity is a CONSTANT equal to (ÿ, ÿ ÿ !Sÿ2ÿ in the negative direction.
This fact is true
(i) regardless the mass of the object.
(ii) only in the absence of air resistance (a vacuum)
.
The initial velocity (vi) of an object that is:
- launched upward is ÿ,ÿ0.ÿ i
,, dropped is ÿZ(ÿ;(ÿJ} ÿ'
* launched downward is ÿÿ,.ÿ e_ e,]aÿ ÿ JO
3. The velocity of a free-falling object at its highest point of motion is -7ÿ ÿ'ÿ)
.
The time for an object to rise from its release point is
its release point.
the time for it to fall back to
AcceUerationlFree FalU
LET'S WORK THESE TOGETHER
1. An airplane accelerates down a runway at 3.20 m/s2 for 32.8 s until is finally lifts off the
ground. Determine the distance traveled before takeoff,
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._ -ÿ.). Oÿ,[xÿ-
"-ÿ Ci-[
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2. A car starts from rest and accelerates uniformly over a time of 5,21 seconds for a distance of
110 m. Determine the acceleration of the car.
j
I--
4 ÿ>. c, t
b -Cÿ
.... I-ÿ ÿ>:>. :L
2
\ c., (. ÿ, 2/, "<ÿ ') '
,.)
./.) o .-
'.>.. 1, l<f'l.!., a
/7, .:1 ÿI'-li
/. 7, I q'll
!
',/ÿ,,Zs-:" s ol
3ÿ Upton Chuck is riding the Giant Drop at Great America, :if Upton free falls for 2,60 seconds,
what will be his final velocity and how far will he fall?
Y-.C,- -ÿ
/!__c- t iÿ -I- c:,(-l
t/.c ÿ
c,M-c\,f ""-t ÿ
\/, -:- O ,<,,I;
V < :-
:ti ..... \'ÿ'"'k'ÿ
AcceJeration/Free Fall
4. A race car accelerates uniformly from 18.5 m/s to 46.1 m/s in 2.47 seconds. Determine the
acceleration of the car and the distance traveled.
t'
'> t,¢.4 ÿ- 2,<(7cÿ
7
<,
J.,
o'/,.: ÿ,r (),'f/] t .1 ÿII,T)() '17]
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L i
\'"
/ I l ! ÿ"-ÿ
.....
5ÿ A feather is dropped on the moon from a height
The acceleration of gravity on
the moon is :[.67 m/sÿ. Determine the time for the feather to fall to the surface of the moon.
/'1 i. \, ÿo
l&_ "ÿrÿ \J, t, , !;> c::t/"
.... I ÿto.
-c;.,W-ÿ7.
..
-rÿ--1, .'D :sc.ÿ-,
6ÿ
Rocket-powered sleds are used to test the human response to acceleration. If a rocket-
powered sled is accelerated to a speed of 444 m/s in L83 seconds, then what is the
acceleration and what is the distance that the sled travels?
Vi:©
\J.C. & t..t t{ t( t.,-,l f
} I.,,,.<:?
( ÿ1 <', o,:" .:; l'\7
t,).c :- t/, .\ ÿf
to "
z]/. :. t j, .I :ÿ;,..,ÿ(
Or'7-"2,
AccelerationlFree Fall
7. A bike accelerates uniformly from rest to a speed of 7.10 m/s over a distance of 35.4 m.
Determine the acceleration of the bike.
!1ÿ-q
Vÿ:v,
'Iÿ 0
70,g ca
t;4,: ÿ"q'-
5ÿO
: -:25;i-
8ÿ An engineer is designing the runway for an airport. Of the planes that will use the airport, the
lowest acceleration rate is likely to be 3 m/s2. The takeoff speed for this plane will be 65 m/s.
Assuming this minimum acceleration, what is the minimum allowed length for the runway?
o, (ÿ rÿ,{(
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91
A car traveling at 22.4 m/s skids to a stop in 2.55 s. Determine the skidding distance of the car
(assume uniform acceleration).
V#-ÿ:ÿO
( Vÿ:-V, .t Qt
"T" S% D- ÿ' -1r4, fÿ, % t
:L0.A kangaroo is capable of jumping to a height of 2.62 m. Determine the takeoff speed of the
kangaroo. (use 9,8 m/s2 for gravity)
b -v,'° ÿ"
4"S\,31->
g 2'1v2'
4ÿS ÿ 'ÿv b