Multiple Representation Problem Solving-4 (Rocket Sled)

A rocket sled used to test automobile restraining devices (seat belts, airaISbions, and so forth) acceleratcs from rest at 8.0 m./s 2 for a distanceof 16 m. In what time interval should the rocket now be stopped so thatthe mamimdc of the avcrage accclemtion is 32 m/s2?

Save space below

PICTORIAL R.EPRESENTAnON

CD(~

6:;1

a~~~a =. --32. rnls "2.

-32.m;s "2.a.=

4-

l~: "0-:.0 ..4

I )c'o ':. O rri

Mi(\tl~ S\~n

jndlC.c;l~ d\red1(t

CG1strUd. a pictoria1lepaeDtatiooof the Iituati~ descn"bed in thepn)blem. ~ude:

.a~uis,

.a Iketd1 that aWl the sled at theinitial aIMi rmal situatioos for ead1 partof the .-oblem,

.Iymbols that ~ie-.t the knownvalues of kinematic quantities at th~

ti-.aIMi.Iymbo1s repr~~Dting the unknownsthat you wish to determine.

'- ~ -"I' v~

x~llo~ ...,~cXy- 7

-.tf ~ ?

b=,?

PHYSICAL REPRESENTATION -fu~

~~

( aca~~ ~ )~orna:

CaJstnJd a ae.-r.re DK)tim1 diagramfm' tbe a1ed duriD& eacb ~ of tbepoblem. U- tbe dUec:tim1S of the

) 8rIOWS iD tbe mOOm1 di8Ir8mI to

dIeCk tbe 8iIDS of tbe qU8Dtities iD

~ pidmia1...J2i~-*..tatimL

~--.,.

1 ~ILI ttt

-

~~@,

I l~vY\ = 0 + 0 + i( "6' ~~2Jt '2.

t;:.2.s

MAm REPRESENTAnONandSOLUTION

a.ooee a ~~~c equltim. that Iel8Iesthe v8riabla involved in the rJnt part ofthe problem. Solve the equation to de-~ mIne needed qIantity that cm1then be used in the ~ ~ of the

poblem.

v

u. the results ofthe previous calcu1a-tim18Dd other information in the pid-mia1..~~OO to determine theUDkDown.

\I.f-'JL~---"

~ -tl(R~\f'j

~2.b+- -2.5

-I(o0/s

~~~~

--1-s2

t-+ ::; 2.5-5

~~IR

EVALUAnON.. .Ik»es tbe siID oftbe 8DSwa' agree

with tbe aituati= s}K)WD iD tbe pidor-

ia1 i~-.t.t:.--il? "{ <2.. 5

.Is tbe 1IDit of the 8DSwa' comd.? y L~

.Is tbe magDitude 18~ble? '\.1 /)S 1T ~ -Q..'('o.e

C AI.PS Kit, Box 4013, Univenity Pt., J

Las Cruces, NM 88003

de.. c-e.1 c2..roJ) 0\1\ -Ir lit L.l s ~ hay- -t +; ~ +0 ~ ~ [).I -23 {¥JJ!~~Q) A FIPSE PIoject'f

to Dote commonerrors.

I x=~:~2 '._.

~4.~

x-= )( c. 0\-- '\( 0"'<:1 + ~a.-*2.

Changing Kinematic Representations-2

(a) An object moves along a horizontal surface.The applia.tion or three kinematic equations tothat motion is shown below .ConstrUct a motiondiagram replaCDliDg the motion and then inventscxne real p~ that might be rcp~ted bythe equations and by the motion diasmm.

9.0 m -O -0 + t<2.0 mts2)t:

(b) An object moves on an incline. The applicationof one kinematic equation to that motion is shownbelow. ConstrUd a motion diagram representingthe motion and then invent some ~ process thatmight be reprcscnted by the equation and by themotion diagram.

-2 (-8.0 m/s1 (x -0)v I -(2.0 m/s2) tl

36 m -9.0 m -VI (t2 -tl)

Solve the equation for the unknown.

\L-'2-4 =:. -12..~~ -=- -1~.()f1.I/l?- ')<

~-+!2- -3

:+i""<;-4x - c I rb M

--:.

Solve the equations for the unknowns.

q\'Y\ :. i (2. O ~~-t12

~ 1..- l.\ -

-61 = 3s .

/ -Vl =. (2 '"I5~ 3.5 ) -

=~

3~ --= lCo~s)(4 I

--~~ "S5lDmW a motion diI8I8aI(s) that is -withthe tiIaDaIic ~tities and with the motiCXldescn"bed by the equatiom. The object is movinghorizon1aUy. y CRl need one motion diI8I8aI foreadI part of the motion-for eadI ~ with adiffercnt accelelation.

-~~ -

-3s "\--"

q :27

Dmw a motion diagram that is amsistcnt with thekinematic quantitim and with the motiondeocribed by the equations. The objectmov~ aJoog an incline.

J;0

/O.::.2M/SZ /...'.--:.,0

I <::"=-- - .q~-~1~~S

--=1>1

-QyVI '=: <0 ~ -" .",. .~ 0.. :::- ° 7s'2

--~-~ 'r--- 3/; -9. ==- 21

Constmd a pictorial ~resentation or someprocess that is oonsistent with the motiondiagIam and the equations above ( there are

many ~ibilities).

c uuct a pictorial reprcsentation of some processthat is consistent with the motion diagram andthe equation above (there are manypossibilities).

A bo-ll (1'(-" to~ c~(' \6\\5 lAp

}h

?l-A""' \1 edCAy-A mQ+~ b~ .\.$

\'n \' ~l)..l

s~~s

3s

-thCt+ i+iStaws

~l t\5r6 u. '\'Y\.Q-

~~ .\-looy-

I -28 (Kinematia) A FIPSE Project