ap physics b - kinematics
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7/18/2019 AP Physics B - Kinematics
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Kinematics
AP Physics B
7/18/2019 AP Physics B - Kinematics
http://slidepdf.com/reader/full/ap-physics-b-kinematics 2/16
Defning the important
variables
Kinematics is a way of describing the motion of objects
without describing the causes. You can describe anobject’s motion:
In words Mathematically Pictorially GraphicallyNo matter HOW we describe the motion, there are several KEY VARAB!E"
that we #se$
Symbol ariable !nitst %ime s
a Acceleration m&s&s
' or y (is)lacement m
vo nitial velocity m&sv *inal velocity m&s
+ or a+ Acceleration d#e to+ravity
m&s&s
7/18/2019 AP Physics B - Kinematics
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The 3 Kinematic equations
%here are ma-or
.inematic e/#ations
than can be #sed to
describe the motion in"#$%I&. All are #sed
when the acceleration
is CONSTANT. )(2
2
1
22
2
oo
oo
o
x xavv
at t v x x
at vv
−+=
++=
+=
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Kinematic #1
at vv
at vvt vv
t va
o
oo
+=
=−−→∆
∆=
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Kinematic #1E'am)le0 % boat mo'es slowly out of a marina (so as to not
lea'e a wa)e* with a speed of +.,- ms. %s soon as itpasses the brea)water/ lea'ing the marina/ it throttles up
and accelerates at 0.1- mss$
2hat do I)now3
2hat do Iwant3
vo1 2$34 m&s v 1 5
a 1 6$74 m&s&s
t 1 3 s
a8 How 9ast is the boat movin+ a9ter acceleratin+ 9or 3 seconds5
=
+=
+=
v
v
at vv o
)5)(40.2()50.1(
+4., ms
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Kinematic #2
221 at t v x x oxo ++=
b* 5ow far did the boat tra'el during that time3
=
++=
++=
x
x
at t v x x oxo
)5)(40.2(
2
1)5)(5.1(0
21
2
2
46., m
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Does all this make sense?
m A
Abh A
50.7
)5.1)(5(
=
=→=
m A
bh A
30
)12)(5(2
1
2
1
=
→=
+.,
ms
+4., ms
m A
Abh A
50.7
)5.1)(5(
=
=→=
$otal displacement 7 6.,- 8 4- 7 46., m 7 $otal %9#% under the line.
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Interesting to Note
vt t v x x
att t v x x
at t v x x
oxo
oxo
oxo
∆++=
++=
++=
21
21
21 2
A 1 HB
A12&6HB
:ost o9 the time, 'o14, b#t i9 it is not
don;t 9or+et to A(( in the initial
)osition o9 the ob-ect$
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Kinematic #3)(222
oo x xavv −+=
2hat do I)now3
2hat do Iwant3
vo1 26 m&s ' 1 5
a 1 <$3 m&s&s
V 1 4 m&s
E'am)le0 You are dri'ing through town at +0 ms when suddenly a ball rolls
out in front of your car. You apply the bra)es and begin decelerating at
4., mss.
5ow far do you tra'el before coming to a complete stop3
=
−=−
−−+=
−+=
x x
x
x xavv oo
7144
)0)(5.3(2120
)(2
2
22
0-.,6 m
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ommon !roblems "tuents$aveI don’t )now which euation to choose;;;
#uation Missing ariable
'
v
t
at vvo +=
2
2
1 at t v x x oxo ++=
)(222
oo x xavv −+=
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Kinematics %or the &'(TI)*Direction All .inematics can be #sed to analy=e one
dimensional motion in either the > direction OR they direction$
)(2)(2
21
21
2222
22
ooy yoox
oyooxo
oy yo
y y g vv x xavv
gt t v y yat t v x x
gt vvat vv
−+=→−+=
++=→++=
+=→+=
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+g, or ag - The )cceleration ue
to gravit.%he acceleration d#e to +ravity is a s)ecial constant that e'ists
in a VA?@@:, meanin+ witho#t air resistance$ 9 an ob-ect isin *REE *A!!, +ravity will <5%=G# an ob-ects velocity by $m&s every second$
2/8.9 sma g g −==
%he acceleration d#e to +ravity0C A!WAY" A?%" (OWNWAR(C" A!WAY" ?ON"%AN% near the
s#r9ace o9 Earth
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'/amples% stone is dropped at rest from the top of a cliff. It is
obser'ed to hit the ground ,.6> s later. 5ow highis the cliff3
2hat do I)now3
2hat do Iwant3
voy1 4 m&s y 1 5
+ 1 <$ m&s6
yo14 m
t 1 3$D s
2hich 'ariable is =?$ gi'en and
=?$ as)ed for3
@inal elocity;
2
21 gt t v y y oyo ++=
=
−=
y
y 2)78.5(9.4)78.5)(0(
A+B4.6 m
5 7+B4.6m
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'/amples% pitcher throws a fastball with a 'elocity of 14., ms. It is
determined that during the windup and deli'ery the ball co'ers adisplacement of 0., meters. $his is from the point behind thebody when the ball is at rest to the point of release. <alculate theacceleration during his throwing motion.
2hat do I)now3
2hat do Iwant3
vo1 4 m&s a 1 5
' 1 6$3 m
v 1 7$3 m&s
2hich 'ariable is =?$ gi'en and
=?$ as)ed for3
$IM#
)(222
oo x xavv −+=
=
−+=
a
a )05.2(205.43 22
46>., mss
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'/amples5ow long does it ta)e a car at rest to cross a 4,.- m
intersection after the light turns green/ if the accelerationof the car is a constant 0.-- mss3
2hat do I)now3
2hat do Iwant3
vo1 4 m&s t 1 5
' 1 3 m
a 1 6$44 m&s&s
2hich 'ariable is =?$ gi'en and
=?$ as)ed for3
@inal elocity
=
++=
t
t 2)2(
2
1)0(035
2
21 at t v x x oxo ++=
,.C0 s
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'/amples% car accelerates from +0., ms to 0, ms in B.-
seconds. 2hat was the acceleration3
2hat do I)now3
2hat do Iwant3
vo1 26$3 m&s a 1 5
v 1 63 m&s
t 1 s
2hich 'ariable is =?$ gi'en and
=?$ as)ed for3
"ISP&%<#M#=$
at vvo +=
=
+=
a
a )6(5.1225
0.-> mss
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