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Less positive means slowing down while going up. More negative means speeding up while going down.. 2""  V]8Xx  x HxQ5?Text Box 11 h|<___PPT11   hdman`  Arial&Monotype Typography 0___PPT10 TThis acceleration vector is the same on the way up, at the top, and on the way down!$U 2U& U V]8Xx$ x #  ? 33___PPT10e+D=' = @B +" R 1 mQeQ |!Q(  >"zSmM |> |  zQ50e0e?Rectangle 10 `p   pKinematics Formula Summary ( x | VXQ5?Rectangle 13L___PPT11,   hdman`  Arial&Monotype Typography 0___PPT10 V "  V]8Xxx | VhF6?Rectangle 15L___PPT11,   hdman`  Arial&Monotype Typography 0___PPT10 V "  V]8Xx | H_R5?Text Box 18P |<___PPT11   hdman`  Arial&Monotype Typography 0___PPT10  (derivations to follow)  2$  V]8XxCx ` |C *Group 23"}A  | F+R5?Text Box 7`P<H<`:___PPT11@:8:   hdman`  Arial&Monotype Typography    hdman`  Arial&Monotype Typography    hdman`  Arial&Monotype Typography    hdman`  Arial&Monotype Typography    hdman`  Arial&Monotype Typography    hdman`  Arial&Monotype Typography    hdman`  Arial&Monotype Typography    hdman`  Arial&Monotype Typography    hdman`  Arial&Monotype Typography    hdman`  Arial&Monotype Typography    hdman`  Arial&Monotype Typography    hdman`  Arial&Monotype Typography    hdman`  Arial&Monotype Typography    hdman`  Arial&Monotype Typography    hdman`  Arial&Monotype Typography    hdman`  Arial&Monotype Typography    hdman`  Arial&Monotype Typography    hdman`  Arial&Monotype Typography    hdman`  Arial&Monotype Typography    hdman`  Arial&Monotype Typography    hdman`  Arial&Monotype Typography    hdman`  Arial&Monotype Typography    hdman`  Arial&Monotype Typography    hdman`  Arial&Monotype Typography    hdman`  Arial&Monotype Typography    hdman`  Arial&Monotype Typography    hdman`  Arial&Monotype Typography    hdman`  Arial&Monotype Typography    hdman`  Arial&Monotype Typography    hdman`  Arial&Monotype Typography    hdman`  Arial&Monotype Typography    hdman`  Arial&Monotype Typography    hdman`  Arial&Monotype Typography    hdman`  Arial&Monotype Typography    hdman`  Arial&Monotype Typography    hdman`  Arial&Monotype Typography    hdman`  Arial&Monotype Typography    hdman`  Arial&Monotype Typography    hdman`  Arial&Monotype Typography    hdman`  Arial&Monotype Typography    hdman`  Arial&Monotype Typography    hdman`  Arial&Monotype Typography    hdman`  Arial&Monotype Typography    hdman`  Arial&Monotype Typography    hdman`  Arial&Monotype Typography    hdman`  Arial&Monotype Typography    hdman`  Arial&Monotype Typography    hdman`  Arial&Monotype Typography    hdman`  Arial&Monotype Typography    hdman`  Arial&Monotype Typography          !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxz{|}~hdman`  Arial&Monotype Typography    hdman`  Arial&Monotype Typography    hdman`  Arial&Monotype Typography    hdman`  Arial&Monotype Typography ___PPT10                vf = v0 + a t vavg = (v0 + vf ) / 2 Dx = v0 t + a t 2 vf2  v02 = 2 a Dx P!0 2$$$ $$( $ " $$&$$(.(,&,$0&0$4.4$8&8$<&<$.$. &$ & &$& &$$ $$$$(($,,$00$44 88$<<$$$  ( $$  $$$$(($,,$00$44$88$<<$( $$$ PV]8Xxd | S A ?? % U  B  | Ro?Line 19 | HR5?Text Box 22@`d___PPT11D<   hdman`  Arial&Monotype Typography    hdman`  Arial&Monotype Typography    hdman`  Arial&Monotype Typography @___PPT10  *For 1-D motion with constant acceleration:@+ 2$$$ + V]8Xx$ | #  ? 33___PPT10u.m+D=' = @B +" y c7 }xux 1x( xc7 8   x8VR50e0e?Rectangle 2 `@   lKinematics Derivations $ T'  H\R5?Rectangle 8p@PP##"___PPT11""   hdman`  Arial&Monotype Typography    hdman`  Arial&Monotype Typography    hdman`  Arial&Monotype Typography    hdman`  Arial&Monotype Typography    hdman`  Arial&Monotype Typography    hdman`  Arial&Monotype Typography    hdman`  Arial&Monotype Typography    hdman`  Arial&Monotype Typography    hdman`  Arial&Monotype Typography    hdman`  Arial&Monotype Typography    hdman`  Arial&Monotype Typography    hdman`  Arial&Monotype Typography    hdman`  Arial&Monotype Typography    hdman`  Arial&Monotype Typography    hdman`  Arial&Monotype Typography    hdman`  Arial&Monotype Typography    hdman`  Arial&Monotype Typography    hdman`  Arial&Monotype Typography    hdman`  Arial&Monotype Typography    hdman`  Arial&Monotype Typography    hdman`  Arial&Monotype Typography    hdman`  Arial&Monotype Typography    hdman`  Arial&Monotype Typography    hdman`  Arial&Monotype Typography    hdman`  Arial&Monotype Typography    hdman`  Arial&Monotype Typography    hdman`  Arial&Monotype Typography    hdman`  Arial&Monotype Typography    hdman`  Arial&Monotype Typography    hdman`  Arial&Monotype Typography    hdman`  Arial&Monotype Typography    hdman`  Arial&Monotype Typography (___PPT10           a = Dv / Dt (by definition) a = (vf  v0) / t vf = v0 + a t"D c$"$$  $ $ $  $$$$(( ,,000$44$88$<<$$$$   $ $$  $$$$(($,,$00$44$88 <<$ DV]8Xx\x PM  C *Group 31"X J   PP5?Rectangle 19PM  T___PPT114,   hdman`  Arial&Monotype Typography    hdman`  Arial&Monotype Typography    hdman`  Arial&Monotype Typography    hdman`  Arial&Monotype Typography    hdman`  Arial&Monotype Typography    hdman`  Arial&Monotype Typography    hdman`  Arial&Monotype Typography    hdman`  Arial&Monotype Typography    hdman`  Arial&Monotype Typography    hdman`  Arial&Monotype Typography    hdman`  Arial&Monotype Typography    hdman`  Arial&Monotype Typography    hdman`  Arial&Monotype Typography    hdman`  Arial&Monotype Typography    hdman`  Arial&Monotype Typography ___PPT10x      :vavg = (v0 + vf ) / 2 will be proven when we do graphing.$; & &&  & . & & .  . $&$ (&( ,&, 0&0 4&4 $8&8:  V]8XxB   Ro?Line 20MMx  VHUR5?Rectangle 29L___PPT11,   hdman`  Arial&Monotype Typography 0___PPT10 V "  V]8Xx4x  P` C *Group 32" P`H3   HP5?Text Box 16 P`/.p-___PPT11P-H-   hdman`  Arial&Monotype Typography    hdman`  Arial&Monotype Typography    hdman`  Arial&Monotype Typography    hdman`  Arial&Monotype Typography    hdman`  Arial&Monotype Typography    hdman`  Arial&Monotype Typography    hdman`  Arial&Monotype Typography    hdman`  Arial&Monotype Typography    hdman`  Arial&Monotype Typography    hdman`  Arial&Monotype Typography    hdman`  Arial&Monotype Typography    hdman`  Arial&Monotype Typography    hdman`  Arial&Monotype Typography    hdman`  Arial&Monotype Typography    hdman`  Arial&Monotype Typography    hdman`  Arial&Monotype Typography    hdman`  Arial&Monotype Typography    hdman`  Arial&Monotype Typography    hdman`  Arial&Monotype Typography    hdman`  Arial&Monotype Typography    hdman`  Arial&Monotype Typography    hdman`  Arial&Monotype Typography    hdman`  Arial&Monotype Typography    hdman`  Arial&Monotype Typography    hdman`  Arial&Monotype Typography    hdman`  Arial&Monotype Typography    hdman`  Arial&Monotype Typography    hdman`  Arial&Monotype Typography    hdman`  Arial&Monotype Typography    hdman`  Arial&Monotype Typography    hdman`  Arial&Monotype Typography    hdman`  Arial&Monotype Typography    hdman`  Arial&Monotype Typography    hdman`  Arial&Monotype Typography    hdman`  Arial&Monotype Typography    hdman`  Arial&Monotype Typography    hdman`  Arial&Monotype Typography    hdman`  Arial&Monotype Typography    hdman`  Arial&Monotype Typography    hdman`  Arial&Monotype Typography    hdman`  Arial&Monotype Typography    hdman`  Arial&Monotype Typography x___PPT10XP             Dx = v t = (v0 + vf) t = (v0 + v0 + a t) t Dx = v0 t + a t 2K 0 $$$  $$$  $$$$(($,,$00$44$88<<$$$$ $$$$$  $$$$((,,$00$4488$ <<$$$$ $$$ $$ $ K V]8XxB   Ro?Line 18 P d  S A ?? 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H P 'Y By py p       QN        ? / D _3zfv9((@                                      '(]gh/|T;+p/>a8a A a y $ T m  0 8 P 'y p      _v9'(9Freeform 42J_L___PPT11,   hdman`  Arial&Monotype Typography 0___PPT10 V "  V]8Xx  H 0?Text Box 43PP___PPT110(   hdman`  Arial&Monotype Typography    hdman`  Arial&Monotype Typography 8___PPT10 p x, 2 "  V]8Xx  \$0?Rectangle 44?L___PPT11,   hdman`  Arial&Monotype Typography 0___PPT10 V "  V]8XxJx `0R   C *Group 52"0`R B   Xo?Line 45P`P B   Xo?Line 46Ppu   Nxr1?Text Box 47`0Dw|<___PPT11   hdman`  Arial&Monotype Typography 0___PPT10 cv  2"  V]8Xxu   NX,?Text Box 48RW |<___PPT11   hdman`  Arial&Monotype Typography 0___PPT10 ct  2"  V]8XxB  XfԔ?Line 49P B  XfԔ?Line 50 0 B  XfԔ?Line 510  $  #  ? 33___PPT10e+D=' = @B +" 6 vn*(     x00e0e?Rectangle 2`   Q Graphing Tips $ B  dԔ?Line 24`tB  dԔ?Line 25`0 : tB  dԔ?Line 26`ti  HY,?Text Box 27`Ph|<___PPT11   hdman`  Arial&Monotype Typography 0___PPT10 eThe same rules apply in making an acceleration graph from a velocity graph. Just graph the slopes! Note: a positive constant slope in blue means a positive constant green segment. The steeper the blue slope, the farther the green segment is from the time axis. 2   V]8XxNx `@ R C *Group 43"@ `RB  Xo?Line 28Pp PB  Xo?Line 29P p y  N(0?Text Box 30`@ D |<___PPT11   hdman`  Arial&Monotype Typography 0___PPT10 ga$ 2c  V]8Xxu  NxF0?Text Box 31 Rg|<___PPT11   hdman`  Arial&Monotype Typography 0___PPT10 ct  2"  V]8XxB  XԔ?Line 32P  B  XԔ?Line 33`0 `B  XԔ?Line 340 P P Jx `0R  C *Group 35"0`R B   Xo?Line 36P`P B   Xo?Line 37Ppu   Na0?Text Box 38`0Dw|<___PPT11   hdman`  Arial&Monotype Typography 0___PPT10 cv  2"  V]8Xxu   Na0?Text Box 39RW |<___PPT11   hdman`  Arial&Monotype Typography 0___PPT10 ct  2"  V]8XxB  XfԔ?Line 40P B  XfԔ?Line 41 0 B  XfԔ?Line 420  $  #  ? 33"K R1 ( zSmM    xh60e0e?Rectangle 2` @   Q Real life  (   Hx0?Text Box 20___PPT11ld   hdman`  Arial&Monotype Typography    hdman`  Arial&Monotype Typography    hdman`  Arial&Monotype Typography    hdman`  Arial&Monotype Typography    hdman`  Arial&Monotype Typography P___PPT100( RNote how the v graph is pointy and the a graph skips. In real life, the blue points would be smooth curves and the green segments would be connected. In our class, however, we ll mainly deal with constant acceleration.P 2    a    V]8XxNx `@ R C *Group 21"@ `RB  Xo?Line 22Pp PB  Xo?Line 23P p y  NH0?Text Box 24`@ D |<___PPT11   hdman`  Arial&Monotype Typography 0___PPT10 ga$ 2c  V]8Xxu  N0?Text Box 25 Rg|<___PPT11   hdman`  Arial&Monotype Typography 0___PPT10 ct  2"  V]8XxB  XԔ?Line 26P  B  XԔ?Line 27`0 `B  XԔ?Line 280 P P Jx `0R  C *Group 29"0`R B   Xo?Line 30P`P B   Xo?Line 31Ppu   NOY,?Text Box 32`0Dw|<___PPT11   hdman`  Arial&Monotype Typography 0___PPT10 cv  2"  V]8Xxu   N6?Text Box 33RW |<___PPT11   hdman`  Arial&Monotype Typography 0___PPT10 ct  2"  V]8XxB  XfԔ?Line 34P B  XfԔ?Line 35 0 B  XfԔ?Line 360  B  dԔ?Line 37`tB  dԔ?Line 38`0 : tB  dԔ?Line 39`t$  #  ? 33" -0 T( .zSmM +   x!00e0e?Rect      !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|~angle 2`   _Area under a velocity graph ( 8x a C *Group 40"aB  Vo?Line 3B  Vo?Line 4ddq  LU0?Text Box 5d|<___PPT11   hdman`  Arial&Monotype Typography 0___PPT10 av 2   V]8Xxq  L(>0?Text Box 6a|<___PPT11   hdman`  Arial&Monotype Typography 0___PPT10 at 2   V]8XxB  Vf>?Line 7dB  Vf>?Line 8R cB  Vf>?Line 9R dcx p C *Group 38"`pB   Xo?Line 110@B   Xo?Line 12`pB  Xo?Line 13  pB  Xo?Line 14pB @ Xo?Line 15p B @ Xo?Line 16p@ B @ Xo?Line 17p 0B @ Xo?Line 18p @   N0?Text Box 19`W '|<___PPT11   hdman`  Arial&Monotype Typography 0___PPT10  forward area " 2&  V]8Xx  N$0?Text Box 20``+|<___PPT11   hdman`  Arial&Monotype Typography 0___PPT10  backward area " 2&  V]8Xx  N10?Text Box 21P {d___PPT11D<   hdman`  Arial&Monotype Typography    hdman`  Arial&Monotype Typography    hdman`  Arial&Monotype Typography @___PPT10  YArea above the time axis = forward (positive) displacement. Area below the time axis = backward (negative) displacement. Net area (above - below) = net displacement. Total area (above + below) = total distance traveled.< 2<$=$c   V]8Xx$  #  ? 33" , hz3 ++H+(     xhX,0e0e?Rectangle 2`@0   FArea  E  H0?Text Box 21` |<___PPT11   hdman`  Arial&Monotype Typography 0___PPT10 AThe areas above and below are about equal, so even though a significant distance may have been covered, the displacement is about zero, meaning the stopping point was near the starting point. 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Therefore, area is in meters!d J  +  V]8Xx~B  Vo?Line 4PPQP~B  Vo?Line 5Q  Lb0?Text Box 6` P___PPT110(   hdman`  Arial&Monotype Typography    hdman`  Arial&Monotype Typography 8___PPT10 sv (m/s)* 2    V]8Xx  L8d0?Text Box 7&sFP___PPT110(   hdman`  Arial&Monotype Typography    hdman`  Arial&Monotype Typography 8___PPT10 qt (s)* 2    V]8Xx~B  VfԔ?Line 8Q~B  VfԔ?Line 9< B  XfԔ?Line 10<  x    C *Group 17"   \8sv*?Rectangle 13@L___PPT11,   hdman`  Arial&Monotype Typography 0___PPT10 V "  V]8Xx~  \X=4?Rectangle 14@|<___PPT11   hdman`  Arial&Monotype Typography 0___PPT10 ^   a  V]8Xx~  \gs*3?Rectangle 15@|<___PPT11   hdman`  Arial&Monotype Typography 0___PPT10 ^   a  V]8Xx~  \H1?Rectangle 16 w|<___PPT11   hdman`  Arial&Monotype Typography 0___PPT10 ^   a  V]8Xx~  \Ȑ0?Rectangle 19  !L___PPT11,   hdman`  Arial&Monotype Typography 0___PPT10 V "  V]8Xx|  b0?Rectangle 20 p p|<___PPT11   hdman`  Arial&Monotype Typography 0___PPT10 ^   a  V]8Xx|  b(0?Rectangle 21P |<___PPT11   hdman`  Arial&Monotype Typography 0___PPT10 ^   a  V]8Xx|  bȼ0?Rectangle 22 P |<___PPT11   hdman`  Arial&Monotype Typography 0___PPT10 ^   a  V]8Xx|  b0?Rectangle 23`P |<___PPT11   hdman`  Arial&Monotype Typography 0___PPT10 ^   a  V]8Xxn  N0?Text Box 24t |<___PPT11   hdman`  Arial&Monotype Typography 0___PPT10 d12 m/s 2   V]8Xxm  NXv3?Text Box 25 @ |<___PPT11   hdman`  Arial&Monotype Typography 0___PPT10 c0.5 s 2   V]8Xxt2  Rw3?Oval 28  L___PPT11,   hdman`  Arial&Monotype Typography 0___PPT10 V "  V]8XxB @ ^Ԕ?Line 29pB @ ^?Line 30Ppr  N(0?Text Box 31WBvw|<___PPT11   hdman`  Arial&Monotype Typography 0___PPT10 h12$ 2e  V]8Xx  H8A+?Text Box 32@ |<___PPT11   hdman`  Arial&Monotype Typography 0___PPT10 h The rectangles under the time axis have negative heights, corresponding to negative displacement. i! 2i" i V]8Xx$  #  ? 33"f; iL2 ::0:( \lf, 4   xCY,0e0e?Rectangle 200    h$Graphs of a ball thrown straight up % %$ %xB  P?Line 3`  PxB  P?Line 4 P xB  P?Line 5p P pxB  P?Line 6P P P i  LD',?Text Box 7`|<___PPT11   hdman`  Arial&Monotype Typography 0___PPT10 ax 2   V]8Xxi  Lk',?Text Box 8p|<___PPT11   hdman`  Arial&Monotype Typography 0___PPT10 av 2   V]8Xxm  L(/?Text Box 9 |<___PPT11   hdman`  Arial&Monotype Typography 0___PPT10 ea" 2a  V]8XxTB   21B CDEF6QRbUVWԔ?CD1uf&H0;C7M*h[qb T3-C$J S Zx +Pp{kQLFER0O-6G/MY]d.iRsRs} * P r   , : J Z a k q w  @                      &HM*bC$ZPkFE6MdRsP , Z q  Freeform 16 L___PPT11,   hdman`  Arial&Monotype Typography 0___PPT10 V "  V]8Xx  Hϕ1?Text Box 17,___PPT11    hdman`  Arial&Monotype Typography    hdman`  Arial&Monotype Typography    hdman`  Arial&Monotype Typography    hdman`  Arial&Monotype Typography    hdman`  Arial&Monotype Typography    hdman`  Arial&Monotype Typography    hdman`  Arial&Monotype Typography    hdman`  Arial&Monotype Typography    hdman`  Arial&Monotype Typography    hdman`  Arial&Monotype Typography    hdman`  Arial&Monotype Typography    hdman`  Arial&Monotype Typography    hdman`  Arial&Monotype Typography ___PPT10ph     0The ball is thrown from the ground, and it lands on a ledge. The position graph is parabolic. The ball peaks at the parabola s vertex. The v graph has a slope of -9.8 m/s2. Map out the slopes! There is more  positive area than negative on the v graph. 2=a!e(a e aaai a $e$5(a(,a, 0a0  V]8Xx^B   <hR1BCDE>FQRUVW?@  `Freeform 18m,4L___PPT11,   hdman`  Arial&Monotype Typography 0___PPT10 V "  V]8Xx6B   {4B&C&DE&F QRUVWo?&&&@ &&&&Freeform 19L___PPT11,   hdman`  Arial&Monotype Typography 0___PPT10 V "  V]8XxB   4B{CDEFQ>R"UVWjJ?{vrl`%F>F>2xO3'd"j#t{ @      {lF>'d{{Freeform 20;uL___PPT11,   hdman`  Arial&Monotype Typography 0___PPT10 V "  V]8XxB @ XjJ?Line 22 B  dfo?Line 24B  XfԔ?Line 250 5 e B  dfo?Line 26 B  XԔ?Line 27  B  dfo?Line 28P  B  dZ?Line 29  B  ^>?Line 300k  Nh1?Text Box 310 |<___PPT11   hdman`  Arial&Monotype Typography 0___PPT10 at 2   V]8Xxk  Nh4?Text Box 32 9 |<___PPT11   hdman`  Arial&Monotype Typography 0___PPT10 at 2   V]8Xxk  N1?Text Box 33P 9 p|<___PPT11   hdman`  Arial&Monotype Typography 0___PPT10 at 2   V]8XxB @ Xfo?Line 34P  P$  #  ? 33"O mf, B:@( zSmM    x00e0e?Rectangle 2``   PGraph Practice    F0?Text Box 3|d \  ___PPT11     hdman`  Arial&Monotype Typography    hdman`  Arial&Monotype Typography    hdman`  Arial&Monotype Typography    hdman`  Arial&Monotype Typography    hdman`  Arial&Monotype Typography    hdman`  Arial&Monotype Typography    hdman`  Arial&Monotype Typography    hdman`  Arial&Monotype Typography    hdman`  Arial&Monotype Typography p___PPT10PH Try making all three graphs for the following scenario: 1. Schmedrick starts out north of home. At time zero he s driving a cement mixer south very fast at a constant speed. 2. He accidentally runs over an innocent moose crossing the road, so he slows to a stop to check on the poor moose. 3. He pauses for a while until he determines the moose is squashed flat and deader than a doornail. 4. Fleeing the scene of the crime, Schmedrick takes off again in the same direction, speeding up quickly. 5. When his conscience gets the better of him, he slows, turns around, and returns to the crash site.X 26ccg g sgvcdgjcf g  X V]8Xx$  #  ? 33___PPT10e+D=' = @B +" ^0 PI( H|@A@ !   xhY10e0e?Rectangle 2 `}   UKinematics Practice    Fh0?Text Box 5P V |<___PPT11   hdman`  Arial&Monotype Typography 0___PPT10 A catcher catches a 90 mph fast ball. His glove compresses 4.5 cm. How long does it take to come to a complete stop? Be mindful of your units! &   V]8Xx|  Z0?Rectangle 7p P L___PPT11,   hdman`  Arial&Monotype Typography 0___PPT10 V "  V]8Xx  FX{0?Text Box 8"PK!{[Content_Types].xml|AN0EH,BI F$- qڲAK{4fg`bhlz39,7U=DdQhVN9GLUHe2!gu]]k(#*kzky_O&鴷Vb\D:r g.dUg3Uc8O.͹᭜&9R~_,dgzjǎ?I'f#®Pb-\/Ƿ0Z]nLnp__3.iJV KQBiDžrL,Vʌ/7р4`ANar+m;E/'3U Aںv83/PK!9qdrs/downrev.xmlDJ1E^MZTiւ t:y3Ilop˽˙-׉#h=kˍ= vIÙ",3,?Ԉ X62V-9ca14 B`BPBpB`B?<*%(/%,( < +D' =1:Bvisible*o3>+#.<*%(D' =+4 8?dCB0-#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*D' =+4 8?dCB0-#ppt_h/2BCB#ppt_yB*Y3>B ppt_y<*+8+0+ +"- 1 ,,`g,( ȷ1 zSmM &   x&A+0e0e?Rectangle 2@   ZUniform Acceleration  k   xh"A+0e0e?Rectangle 30  When object starts from rest and undergoes constant acceleration: Position is proportional to the square of time. Position changes result in the sequence of odd numbers. Falling bodies exhibit this type of motion (since g is constant).pB  B083    V]8XxxB  P?Line 4 P xB  P?Line 5PPxB  P?Line 6U  Fh4A+?Text Box 7'x___PPT11XP   hdman`  Arial&Monotype Typography    hdman`  Arial&Monotype Typography    hdman`  Arial&Monotype Typography    hdman`  Arial&Monotype Typography H___PPT10(  ot : 0 1 2 3 4Np   ma e  p V]8Xx  FA+?Text Box 9@`x___PPT11XP   hdman`  Arial&Monotype Typography    hdman`  Arial&Monotype Typography    hdman`  Arial&Monotype Typography    hdman`  Arial&Monotype Typography H___PPT10(   Dx = 1V 2 $   V]8Xx  HxkA+?Text Box 100x___PPT11XP   hdman`  Arial&Monotype Typography    hdman`  Arial&Monotype Typography    hdman`  Arial&Monotype Typography    hdman`  Arial&Monotype Typography H___PPT10(   Dx = 3V 2 $   V]8Xx  HxeA+?Text Box 11 x___PPT11XP   hdman`  Arial&Monotype Typography    hdman`  Arial&Monotype Typography    hdman`  Arial&Monotype Typography    hdman`  Arial&Monotype Typography H___PPT10(   Dx = 5V 2 $   V]8Xxz  Hh4?Text Box 120P|<___PPT11   hdman`  Arial&Monotype Typography 0___PPT10 v( arbitrary units )  2$  V]8XxzB  R?Line 1300zB  R?Line 14  HvA+?Text Box 17@`P___PPT110(   hdman`  Arial&Monotype Typography    hdman`  Arial&Monotype Typography 8___PPT10 yx : 0 1 4 9 16 6z 2$ye z V]8XxzB  R?Line 18   H(\$?Text Box 19x___PPT11XP   hdman`  Arial&Monotype Typography    hdman`  Arial&Monotype Typography    hdman`  Arial&Monotype Typography    hdman`  Arial&Monotype Typography H___PPT10(   Dx = 7V 2 $   V]8XxB  X1?Line 200 $  #  ? 33___PPT10e+D=' = @B +"P 1 C;p(  !   x 00e0e?Rectangle 2M=   USpreadsheet Problem  \   x00e0e?Rectangle 3  We re analyzing position as a function of time, initial velocity, and constant acceleration. x, Dx, and the ratio depend on t, v0, and a. Dx is how much position changes each second. The ratio (1, 3, 5, 7) is the ratio of the Dx s. x ]   $$((,,004488,<<, #  V]8Xx`  c $A  ??@ %    F(#?Text Box 6` g   ___PPT11     hdman`  Arial&Monotype Typography    hdman`  Arial&Monotype Typography    hdman`  Arial&Monotype Typography    hdman`  Arial&Monotype Typography    hdman`  Arial&Monotype Typography    hdman`  Arial&Monotype Typography    hdman`  Arial&Monotype Typography    hdman`  Arial&Monotype Typography    hdman`  Arial&Monotype Typography    hdman`  Arial&Monotype Typography    hdman`  Arial&Monotype Typography ___PPT10`X    Make a spreadsheet like this and determine what must be true about v0 and/or a in order to get this ratio of odd numbers. Explain your answer mathematically.! 2E   + $$$((  V]8Xx$  #  ? 33___PPT10e+D=' = @B +"S# 1 """(  hđ1    x>',0e0e?Rectangle 2`   Q Relationships ( 2!  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