PROBLEMS ON RECTILINEAR MOTION
PROBLEM 1. The elociy of a paricle which oe along he -ai i gien by 5 (/). Ealuae he diplaceen elociy and acceleraion a when = 4. The paricle i a he origin = when =. (/) /
SOLUTION 5 / (/) calculae and acceleraion a when = 4. The paricle i a he origin = when =. 5 d d / 5 5 f ( ) dd 5/ d 5/ 5 4 / d 8647 5 / f ( ) 4 4 4 / d d a 4 a 15 / a 5 1/ 7.5 1/
PROBLEM. The elociy of a paricle which oe along he -ai i gien by 4 / where i in econd. Calculae he diplaceen D of he paricle during he ineral fro = o = 4. (/6)
SOLUTION 4 d 4 diplaceen D fro = o = 4. 4 4 16 4 4 d D 4 d d d d 4(4) 4 64 8 8 4 4()
PROBLEM. A ball i hrown erically upward wih an iniial peed of 5 / fro he bae A of a 15- cliff. Deerine he diance h by which he ball clear he op of he cliff and he ie afer releae for he ball o land a B. Alo calculae he ipac elociy B. Neglec air reiance and he all horizonal oion of he ball. (/1)
SOLUTION =5 / deerine diance h ie afer releae for he ball o land a B and ipac elociy B C A - C g ( y y) 65 94.19.6h h 16. 86 a ( 5 ) a g (9.81) (15h).7 19.6h A - B 1 1 y y g 155 (9.81) 4.95 5 15 4.4.69 1 y g B 59.81(4.4) 18.16 / ( )
PROBLEM 4. In he pinewood-derby een hown he car i releaed fro re a he aring poiion A and hen roll down he incline and ono he finih line C. If he conan acceleraion down he incline i.75 / and he peed fro B o C i eenially conan deerine he ie duraion AC for he race. The effec of he all raniion area a B can be negleced. (/14)
ie duraion AC for he race a a C B d d ad d a a c a B A BC AB oal BC BC BC BC BC B B BC C B BC B B B AB AB AB AB AB AB AB AB A A AB A AB B.46.985 1.477.985 4.6 4 1 / 4.6 16.5 (.75)().75.75 1.477 (.75) 1 1 1 /.75 SOLUTION
PROBLEM 5. A paricle ar fro re a = - and oe along he -ai wih he elociy hiory hown. Plo he correponding acceleraion and he diplaceen hiorie for he econd. Find he ie when he paricle croe he origin. (/9)
1.97 1.75 1.5 SOLUTION ie when he paricle croe he origin.5 1 a 1 (6)(.5).5 1. 5 fro.5 1.5.417 oal.5.417.917 a / 6.5 1.5 1.75-4 - -1.5
PROBLEM 6. Car A i raelling a a conan peed A = 1 k/h a a locaion where he peed lii i 1 k/h. The police officer in car P obere hi peed ia radar. A he oen when A pae P he police car begin o accelerae a he conan rae of 6 / unil a peed of 16 k/h i reached and ha peed i hen ainained. Deerine he diance required for he police officer o oerake car A. Neglec any nonrecilinear oion of P. (/)
A = 1 k/h (conan) a he oen when A pae P P begin o accelerae a conan rae of 6 / unil a peed of 16 k/h i reached hen ainained deerine diance required for P o oerake A. 1k / h6.11 / 16k/ h44.44 / For A A o 6. 11 For P 44.44 6 P o a 7.47 1 1 o a 6(7.47) 164.59 hen ap P o ( 7.47) 164.5944.44( 7.47) When P cache A A = P 6.11 164.5944.44( 7.47) 44.44 164.577 164.5778. 19.757 71.4 () P =f() 71.4 A =f() 164.59 (/) 44.44 6.11 a (/ ) 6 7.47 19.757 A a A P a P () () ()
PROBLEM 7. A rearding force i applied o a body oing in a raigh line o ha during an ineral of i oion i peed decreae wih increaed poiion coordinae according o he relaion k / where k i a conan. If he body ha a forward peed of 5 / and i poiion coordinae i 5 a ie = deerine he peed a =. (/)
Due o a rearding force peed decreae wih increaed poiion coordinae according o k / d d and k a (k conan). If = 5 / (frw) = 5 a = deerine a = k/ 5 / 1/ d k / 1/ k/ 5 k k 565 d 75115 1/ 1/ 1/ 1/ d k 75 75115 d f ( ) 75/ 9.69 / 1/ d / 75/ 1/ / 5 d 5 75115 / 1/1/ 75115 1 k 75115 1/ / 1/ 1/ 5 1/ d d
PROBLEM 8. The cone falling wih a peed rike and penerae he block of packing aerial. The acceleraion of he cone afer ipac i a = g cy where c i a poiie conan and y i he peneraion diance. If he aiu peneraion deph i obered o be y deerine he conan c. (/45)
? ) ( a c y y y f cy g a final iniial SOLUTION 6 1 y y gy c gy cy gy cy cy gy dy cy g d ady d
PROBLEM 9. The brake echani hown in he figure i copoed of a pion oing in a fied cylinder filled wih oil. When he brake pedal i preed while he ehicle oe wih a peed he pion oe oil pae hrough he channel inide he pion and he ehicle low down in proporion o i peed a=-k. Deerine a) in er of b) in er of c) in er of. Alo conruc he relaed graphic. pion oil
iniial peed a=-k. Deerine a) in er of b) in er of pion c) in er of. Alo conruc he relaed graphic a) =f()=? a d d e d ln o k e f ( ) k d k e d d ln o k k d kd oil b) =f()=? d d d k f ( ) e 1e k k d d d e k k e k d e k k e d k 1 k e a d e a a
iniial peed a=-k. Deerine a) in er of b) in er of c) in er of. Alo conruc he relaed graphic pion c) =f()=? dad d kd k f ( ) dkd dkd k dk d oil k
PROBLEM 1. A buper coniing of a ne of hree pring i ued o arre he horizonal oion of a large a which i raeling a 4 / a i conac he buper. The wo ouer pring caue a deceleraion proporional o he pring deforaion. The cener pring increae he deceleraion rae when he copreion eceed.5 a hown on he graph. Deerine he aiu copreion of he ouer pring. (/55)
SOLUTION d ad =4 / aiu copreion of he ouer pring 4 d ad area under a cure z.5.5 z.5.5 z
SOLUTION 1 =4 / aiu copreion of he ouer pring d 16 4 4.5.81 ad 16 5 1 5 ( 4.5 4.75 1 4 d 1 1(.5) 41 11 1.1.5) ad.5 area z (.5)(.5) 1( 1( under.5) 1 a cure.5)
PROBLEM 11. The preliinary deign for a rapid-rani ye call for he rain elociy o ary wih ie a hown in he plo a he rain run he. k beween aion A and B. The lope of he cubic raniion cure (which are of for a+b+c +d ) are zero a he end poin. Deerine he oal run ie beween he aion and he aiu acceleraion. (/58) 1
SOLUTION lope of a+b+c +d for cure zero a end poin deerine oal run ie beween he aion and he aiu acceleraion f ( ) a b c d iniial and final condiion gie he conan a a d d a b c d ( a 15 ) b hen c d c(15) d(15) c 675d 1 c 675d c.5d
SOLUTION 4 56.5 15.64.96 (.14 ) (.481) ) (.14.481 ) ( /.481 /.14 1687.5 75 ).5 5( 6.11 75 5 (15) (15) / 6.11 / 1 d d f a f c d d d d d c d c d c h k d d d f d d 71 4.14.481.14.481 ) ( 15 4 15 he diance he rain rael in he fir and la 15 econd 1
SOLUTION when he peed i conan he rain rael 1 a 658 6.11 7. 61 oal run ie (71)=658 oal (15) 7.61 1. 61 1 Maiu acceleraion a da d a f ( ).96.64.96 (.64 ) 7.5 a 7.5 da d.96(7.5).64 (7.5).61 /