MODUL 20 / TG5: GERAKAN PADA PADA GARIS LURUS
KERTAS KERTAS 2
1. Satu zarah, P zarah, P,, br!ra" #$ %&a'(a'! %atu !ar$% )uru% #'!a' ha)a(u v *%+1, #$br$ )h v - − t 2, #'!a' "a#aa' t $a)ah $a)ah *a%a, #a)a* %aat, %)&a% *)a)u$ t$t$" tta& O. A particle particle P moves in a straight line line with velocity, velocity, v * v * % 1 is given by v - − t 2, where t is −
the time, in seconds, after passing through O ' th )$'. ar$, $'#, a ha)a(u a3a), #a)a* *% +1 , zarah P zarah P . the initial velocity, in *%+1 , of , of particle P.
41 * /Ara% R
b &6uta' zarah P zarah P %)&a% %)&a% %aat. the acceleration of P after 4 seconds.
42 * / Ara% R
6 (ara" zarah P zarah P #ar$ #ar$ O %)&a% 7 %aat. the distance of P from O after 6 seconds. seconds .
4 * / Ara% S
# (ara" P (ara" P #ar$ #ar$ O a&ab$)a zarah P brh't$ %"t$"a the distance of P from O when P is instantaneous at rest . rest .
48 * / Ara% T
2. Sb$($ batu #$)u'6ur"a' #$)u'6ur"a' %6ara *'6a'6a'! *'6a'6a'! " ata% #'!a' "a#aa' "#u#u"a''9a #ar$ )a'ta$ %)&a% t % #$br$ )h s )h st = ;t ;t − .t .t 2 *tr, t ≥ 0. A stone is proected vertically upwards so that its position above the
s st *
ground level level after t seconds is given given by s st = ;t ;t − .t .t 2 *tr%, t ≥ 0. a ar$ (ara" (ara" batu #ar$ )a'ta$ )a'ta$ %)&a% 5 %. !ind the distance distance of the stone from from the ground level after " s. s.
41 * / Ara% R b ar$ ha)a(u a3a) batu $tu. !ind the initial velocity of the stone
48 * / Ara% R
6 ar$ t$'!!$ *a"%$*u* batu $tu. !ind the ma#imum ma#imum height reached reached by the stone.
48 * / Ara% S
# ar$ *a%a 9a'! 9a'! #$a*b$) )h batu $tu u'tu" *'!h'ta* *'!h'ta* )a'ta$. )a'ta$. !ind the time ta$en for the stone stone to hit the ground.
42 * / Ara% S
A&a 9a'! b)h b)h #$"ata"a' #$"ata"a' t'ta'! &6uta' batu batu $tu< %hat can you say about the acceleration of the stone&
41 * / Ara% S
MODUL SOLA MATEMATIK MATEMATIK TAM=A>AN 201
M20+
1
MODUL 20 / TG5: GERAKAN PADA GARIS LURUS 8. Satu zarah br!ra" #$ %&a'(a'! %atu !ar$% )uru% #a' *)a)u$ t$t$" tta& O. >a)a(u'9a v m s− ' , #$br$ )h v - 1.t −0.8t 2 ? 0.5, #'!a' "a#aa' t ia)ah *a%a, #a)a* %aat, %)&a% *)a)u$ t$t$" O. A particle moves along a straight line and passes through a fi#ed point O. (ts velocity, v * % 1 is given by v - 1.t −0.8t 2 ? 0.5, where t is the time in seconds after passing −
through O. ar$ !ind a &6uta' , #a)a* *% 2, ba!$ zarah $tu %)&a% 2%. −
the acceleration of the particle, in *% 2, after 2 %. −
42 * /Ara% R
b '$)a$ t a&ab$)a zarah $tu brh't$ %"t$"a. the value of t when the particle comes instantaneously to rest 48 * /Ara% S 6 (u*)ah (ara" #$)a)u$, #a)a* *, #ar$ t - 0 %h$'!!a t - 10 the total distance travelled, in m, by the particle from t - 0 and t - 10. 45 * /Ara% T
. Suatu zarah br!ra" %&a'(a'! %uatu !ar$% )uru% #a' *)a)u$ %atu t$t$" tta& O. >a)a(u'9a, v *% −1 , #$br$ )h v = ; + 2t − t 2 , #'!a' "a#aa' t $a)ah *a%a, #a)a* %aat, %)&a% *)a)u$ O. @arah $tu brh't$ %"t$"a #$ %uatu t$t$" ) . A &art$6) *% a)'! a %tra$!ht )$' a'# &a%%% thru!h a B$C# &$'t O. It% )6$t9, v *% , $% !$' b9 v = ; + 2t − t 2 , 3hr t $% th t$*, $' %6'#%, aBtr &a%%$'! thru!h O . Th &art$6) %t&% $'%ta'ta'u%)9 at &$'t ) . 4A'!!a&"a' !ra"a' " arah "a'a' %ba!a$ &%$t$B. 4 Assume motion to the right is positive. −1
ar$/ !ind a &6uta', #a)a* *%+2, ba!$ zarah $tu #$ ). the acceleration, in *%+2, of the particle at ). 48 * /Ara% S +1 b ha)a(u *a"%$*u*, #a)a* *% , ba!$ zarah $tu. the ma#imum velocity, in *%+1, of the particle. 48 * /Ara% S 6 (u*)ah (ara", #a)a* *, 9a'! #$)a)u$ )h zarah $tu #a)a* 10 %aat &rta*a, %)&a% *)a)u$ O. the total distance, in m, travelled by the particle in the first 10 seconds, after passing through O. 4 * /Ara% T
MODUL SOLA MATEMATIK TAM=A>AN 201
M20+
2
MODUL 20 / TG5: GERAKAN PADA GARIS LURUS 5. Suatu zarah br!ra" #$ %&a'(a'! %atu !ar$% )uru% #a' *)a)u$ t$t$" tta& O #'!a' ha)a(u 20 *%+1. P6uta''9a, a *% −2 , #$br$ )h, a - 2t ? ; #'!a' "a#aa' t $a)ah *a%a, #a)a* %aat, %)&a% *)a)u$ t$t$" O. @arah $tu brh't$ %)&a% p % A particle moves along a straight line and passes through a fi#ed point O, with velocity of 20 *% −1 . (ts acceleration, a *% −2 , is given by a - 2t ? ; where t is the time, in seconds, after passing through point O. *he particle stops after p s. a
ar$/ !ind :
$ ha)a(u *a"%$*u* zarah $tu. the ma#imum velocity of the particle , $$ '$)a$ p. the value of p
47 * /Ara% S
b
La"ar"a' !raB ha)a(u+*a%a ba!$ !ra"a' zarah $tu ba!$ 0 t p. Stru%'9a, atau #'!a' 6ara )a$', h$tu'!"a' (ara" 9a'! #$)a)u$ #a)a* t*&h tr%but. +$etch a velocitytime graph of the motion of the particle for 0 t p. -ence, or otherwise, calculate the total distance travelled during that period . 4 * /Ara% T
7. Suatu zarah br!ra" %&a'(a'! !ar$% )uru% #'!a' "a#aa' ha)a(u'9a, v *%+1 %)&a% *'$'!!a)"a' t$t$" tta& O t % "*u#$a', #$br$ )h v - 7 ? $t − t 2 , #$ *a'a $ a#a)ah &*a)ar. @arah $tu brh't$ %"t$"a #$ t$t$" A, 7 % %)&a% *'$'!!a)"a' O. A particle moves in a straight line so that, t second after leaving a fi#ed point O, its velocity, v ms' , is given by v - 7 ? $t − t 2 , where $ is a constant. *he particle comes to instantaneous rest at point A, 6 seconds after leaving O. a
ar$ '$)a$ $. valute $.
b ar$ &6uta' zarah #$ A. /alculate the acceleration of the particle at A.
42 * /Ara% R
42 * /Ara% R
6 ar$ ha)a(u *a"%$*u* zarah $tu. !ind the ma#imum velocity of the particle. # ar$ (ara" OA. /alculate the distance OA.
MODUL SOLA MATEMATIK TAM=A>AN 201
48 * /Ara% S
48 * /Ara% S
M20+
8
MODUL 20 / TG5: GERAKAN PADA GARIS LURUS F. Sbuah bt br!ra" #$ %&a'(a'! !ar$% )uru% #a' '($''9a #$*at$"a' &a#a *a%a t - 0. 100 +1 >a)a(u'9a #a)a* * % +1 %)&a% t %aat #$br$ )h v = 2 *% , t ≥ 0. t + 2 A boat travelling in a straight line has its engine turned off at time t - 0. (ts velocity in * %+1 after t seconds is then given by
v =
100 t + 2 2
, t ≥ 0.
a ar$ ha)a(u a3a) #a' ha)a(u %)&a% 8 %aat bt $tu. !ind the initial velocity of the boat, and its vvelocity after 1 seconds. 48 * /Ara% R b ar$ bra&a )a*a"ah *a%a 9a'! #$a*b$) )h bt $tu u'tu" br!ra" %(auh 80 *. 45 * /Ara% T !ind how long it ta$es for the boat to travel 10 metres.
6 ar$ &6uta' bt $tu %)&a% 2 %aat. !ind the acceleration of the boat after 2 seconds.
42 * / Ara% S
;. Ra(ah *'u'(u""a' "#u#u"a' #a' arah !ra"a' #ua b(", A #a' 3, 9a'! br!ra" &a#a %uatu !ar$% )uru% #a' *a%$'!+*a%$'! *)a)u$ #ua t$t$" tta& P #a' . Pa#a "t$"a A *)a)u$ t$t$" tta& P , 3 *)a)u$ t$t$" tta& . ara" P $a)ah 0 *. *he following diagram shows the positions and directions of motion of two obects, A and 3, moving in a straight line passing two fi#ed points, P and , respectively. Obect A passes the fi#ed point P and obect 3 passes the fi#ed point simultaneously. *he distance P is 0 *.
A
B
P
M
H
0 *
>a)a(u A, 5 A * %+1 , #$br$ )h
5 A
=
10 + ;t − 2t 2 , #'!a' "a#aa' t $a)ah *a%a , #a)a*
%aat, %)&a% *)a)u$ P , *a'a"a)a = br!ra" #'!a' ha)a(u *a)ar −8 * %+1. Ob(" A brh't$ %"t$"a #$ ). *he velocity of A,
5 A
* % −1 , is given by
5 A
=
10 + ;t − 2t 2 , where t is the time, in
seconds, after it passes P while 3 travels with a constant velocity of
8 * % +1. Obect A
−
stops instantaneously at point ). A'!!a&"a' !ra"a' " arah "a'a' %ba!a$ &%$t$B. Assume that the motion towards the right is positive.
MODUL SOLA MATEMATIK TAM=A>AN 201
M20+
MODUL 20 / TG5: GERAKAN PADA GARIS LURUS
ar$ !ind a ha)a(u *a"%$*u*, #a)a* * % +1 ba!$ A. the ma#imum velocity , in, * % −1 , of A,
48 * / Ara% R
b (ara", #a)a* *, ) #ar$ P . the distance, in *, of ) from P ,
4 * / Ara% S
6 (ara", #a)a* *, a'tara A #a' 3 "t$"a A bra#a #$ t$t$" ). the distance, in *, between A and 3 when A is at the points ) .
48 * / Ara% T
. Ra(ah #$ ba3ah *'u'(u""a' %%ara' ba!$ #ua zarah, P #a' H, 9a'! br!ra" %r'ta" " "a'a' %atu t$t$" tta& O, #$ %&a'(a'! %uatu !ar$% )uru%. *he diagram shows the displacements of two particles, P and , moving simultaneously to the right of a fi#ed point, O, along a straight line. s *
+ + P
0
5
t %
D$br$ %%ara' zarah P #a' zarah *a%$'!+*a%$'! $a)ah s p = at − t 2 #a' s = '."t, #'!a' "a#aa' t $a)ah *a%a #a)a* %aat %)&a% *'$'!!a)"a' O. ar$ iven that the displacement of the particles P and are s p = at − t 2 and s = '."t respectively, where t is the time in second after leaving O. !ind a '$)a$ a, value of a.
42 * / Ara% R
b ha)a(u a3a) zarah P. initial velocity of particle P.
42 * / Ara% R
6 *a%a a&ab$)a zarah P #a' zarah brt*u %)&a% *'$'!!a)"a' O. the time when the particle P dan meet after leaving O. 48 * / Ara% S # (ara" #$)a)u$ )h zarah P %)&a% 5 %. distance travelled by particle P after " s.
MODUL SOLA MATEMATIK TAM=A>AN 201
48 * / Ara% T
M20+
5
MODUL 20 / TG5: GERAKAN PADA GARIS LURUS 10. Satu zarah br!ra" #$ %&a'(a'! !ar$% )uru% #'!a' "a#aa' ha)a(u'9a %)&a% *)a)u$ t$t$" tta& O, t %aat "*u#$a' #$br$ )h v =
20 2t + 2
. ar$
A particle moves in a straight line so that, t seconds after passing through a fi#ed point O, its velocity, v *% 1, is given b9 v =
20 2t + .
2
. !ind
a $ ha)a(u zarah &a#a O, the velocity of the particle at O , $$ a#a"ah zarah br&atah ba)$" %)&a% *)a)u$ t$t$" O< will the particle change direction after passing O&
48 * / Ara% R
b &6uta' zarah a&ab$)a t - 8, the acceleration of the particle when t - 8,
48 * / Ara% S
6 (ara" 9a'! #$)a)u$ )h zarah #a)a* ; %aat 9a'! &rta*a, the distance travelled by the particle in the first 7 seconds .
4 * / Ara% T
MODUL SOLA MATEMATIK TAM=A>AN 201
M20+
7
