University Physics AI No. 1 Rectilinear Motion

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1 Uniesity Physics AI No. Rectiline Motion Clss Numbe Nme I.Choose the Coect Answe. An object is moing long the is with position s function of time gien by (. Point O is t. The object is efinitely moing tow O when ( C ) ( ) ( ) (A) <. (B) >. (C) <. (C) >. Solution: If the object is moing tow O, the elocity n the position ecto of the object he iffeent iection. Tht is <, so the nswe is C..An object stts fom est t when t. The object moes in the iection with positie elocity fte t. The instntneous elocity n ege elocity e elte by ( D ) (A) / < / t. (B) / / t. (C) / > / t. (D) / cn be lge thn, smlle thn, o equl to /t. Solution: The instntneous elocity n ege elocity e both positie, the mgnitue of them cn not be compe. 3. An object is moing in the iection with elocity (, n is nonzeo constnt. With when t, then fo t > the quntity / is ( C ) (A) Negtie. (B) Zeo. (C) Positie. (D) Not etemine fom the infomtion gien. Solution: As when t, then fo t > the elocity ( hs the sme iection with. So we he >, the nswe is C. II. Filling the Blnks. The mgnitue of the cceletion of spots c tht cn g ce fom est to km/h in 5.s is 5/9m/s o 5.56m/s. Assume the cceletion is constnt, lthough typiclly this is not goo ssumption fo utomobiles. The tio of the mgnitue of this cceletion to the mgnitue of the locl cceletion ue to gity (g 9.8 m/s ) is.57. Solution: Accoing to the efinition of the cceletion

2 t 3 / (m/s ) / 9 The tio is The -component of the position ecto of pticle is shown in the gph in Figue s function of time. () The elocity component t the instnt 3. s is (m) -4m/s. Is the elocity component zeo t ny time? yes If so, 4 the time is.5s. If not, eplin why not,. (c) Is the pticle lwys moing in the sme iection long the -is? No If so, eplin wht les you to this 3 conclusion. If not, the positions t which the Fig. pticle chnges iection is 5m, t.5s. Solution: () Accoing to the efinition of the instntneous ( 6 elocity, tngent to gph t t3s, so 4m/s..5 Becuse the tngent t t.5s is zeo. (c) Accoing to the tngent of the gph, the elocity is positie uing t<.5s n negtie uing t>.5s 3. When io we impinges on the ntenn of you c, electons in the ntenn moe bck n foth long the ntenn with elocity component s shown b f schemticlly in Figue. Roughly sketch the sme gph e g t n inicte the time instnts when c () The elocity component is zeo;, c, e, g h The cceletion component is zeo; b,, f, h Fig. (c) The cceletion hs its mimum mgnitue., c, e, g Solution: () See the gph. (c) Accoing to the efinition of the cceletion, tngent to gph, we cn wing the conclusion. 4. The gphs in Figue 3 epict the elocity component of t in one-imensionl mze s function of time. You tsk is to mke gphs of the coesponing

3 (m/s) (m/s) (m/s) (m/s) () (m/s) (c) Fig.3 () (e) (i) Acceletion component esus time Solution: Using the efinition of the cceletion. (m/s ) (m/s ) (m/s ) () (c) (m/s ) (m/s) () (e) (ii) The -component of the position ecto esus time. In ll cses ssume m when ts.

4 Solution: Using t + t + n + t (, we he () t (s < t < s) 4 (s t 3s) t (3s < t < 4s) HmL 4 3 thsl 3 4 t t t + 4 HmL (s < t < s) (s t < 4s) 3 4 thsl (e) (c) t + t () HmL thsl t 4 t (s < t < s) (s t < 4s).5.5 t + t (s < t < s) 4t t 6 (s t < 4s) m - HmL 3 4 thsl 3 4 thsl III. Gie the Solutions of the Following Poblems

5 . Hng mss on eticl sping; imgine n oigin t the plce whee the mss is t est with î iecte own s shown in Figue 4. Now set the mss into oscilltion in the eticl iection by loweing the mss istnce A n letting it go. The subsequent motion is clle simple hmonic oscilltion n will be inestigte in some etil in Chpte 7. A We shll see tht the position ecto of pticle eecuting such one-imensionl oscilltoy motion is gien by the epession î [ Acos( ], whee A is epesse in metes, n is epesse Fig.4 in ins pe secon; both e constnts. () Fin the elocity ecto n the cceletion ecto s function of time. Wht e the getest mgnitues of the elocity n cceletion ectos? (c) Wht is the eliest (nonnegtie) time tht the position ecto ttins mimum mgnitue? When the position ecto hs its getest mgnitue, wht is the mgnitue of the elocity ecto? Wht is the mgnitue of the cceletion ecto t the sme time? () At wht time ( t s ) oes the position ecto fist ttin mgnitue of m? At this time, wht e the mgnitues of elocity n cceletion ectos? Solution: () The elocity ecto is [ Acos( ]ˆ i [ Asin( ]. The cceletion ecto is ( [ Asin( ]ˆ i [ Acos( ] (c) Using m )] m [ Asin( t A [ Acos( t A m )] m [ Acos( ], so when cos(, we he [ Acos( t A. k Thus t ± k k,,,... n t ± k,,,... m )] m Thinking the subsequent motion fom beginning, so we neglect ts. The eliest time is t ( k ) tht the position ecto ttins mimum mgnitue. At the sme time, the mgnitue of the elocity ecto is Asin( Asin( ) m/s. The mgnitue of the cceletion ecto is

6 () Using Acos( Acos( ) A [ Acos( ], so when cos(, we he Acos(. k Thus t ± k k,,,... n t ± k,,,... Then the time is tmin ( k ) uing mgnitue of m. At this time, the mgnitue of the elocity ecto is t s t which the position ecto fist ttin Asin( Asin( ) A m/s. The mgnitue of the cceletion ecto is Acos( Acos( ) m/ s. One moel fo the motion of pticle moing in esistie meium suggests tht the spee t ecese eponentilly ccoing to the epession e, whee is the spee of the pticle when t s n is positie constnt. () How long will it tke the pticle to ech hlf its initil spee? Wht istnce oes the pticle tese uing the time intel clculte in pt ()? (c) Though wht istnce oes the pticle moe befoe it is bought to est? Solution: () ( t ln t The istnce tht the pticle tese is ln t t e e S ln ( ln e t e ln t ( e ln ) (c) Accoing to the epession t e, When t,. The istnce the pticle moes befoe it is bought to est is S ( e e ( ) -t -t

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