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习题练习:Physics Bowl by Topic 2: Kinematics - part I General Motion

 作者: admin   总分: 72分  得分: _____________

答题人: 游客未登录  开始时间: 24年03月31日 09:50  切换到: 整卷模式

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1#
 
单选题 ( 1.0 分) 切至整卷模式 搜藏此题  
  10.10: A particle travels at a constant speed around a circular path ofv;topj tr3gh0r .,h j-3mic8j7 fi g0u radius $R$, if the particle makes one complete trip around the entire circle, what is the magnitude of the displacement for this trip?

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2#
 
单选题 ( 1.0 分) 切至整卷模式 搜藏此题  
  99.01: The change of distance per unit time without reference to a particula;3ua / tk4bbit; jvgx ;2wbz(gr dire/jv uxgb3tb 2k gz;;iwb(4ta;ction is called

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3#
 
单选题 ( 1.0 分) 切至整卷模式 搜藏此题  
  12.29: A vehicle completes one lap around a circular track at an a +lfytt:e8k,f5f (vs -o)x(h q nv)dppverage speed of 50 m/s and then completes a second lap at an average spes ,y8(:t5nfot lefdf pq vp)k)+-v( xhed of $V$. The average speed of the vehicle for the completion of both laps was 80 m/s. What was the average speed $V$ of the second lap?

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4#
 
单选题 ( 1.0 分) 切至整卷模式 搜藏此题  
  95.03: A toy car moves 0.80 m in 1.0 s at the constant velnx6q0t 4dm8w focity. If it continues, how far will it travel in 3.0 q x8t04fdm6nw s?

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5#
 
单选题 ( 1.0 分) 切至整卷模式 搜藏此题  
  05.34: A 40-kg boy is stational2bk j,mm*oz jp9h -e9ry on a 30-kg plank that is sliding at 5.00 m/s to the right across a frictionless pond. The bbjop*2kem9z,h-lm 9j oy then turns and starts walking on the plank at a rate of 4.00 m/s to the left, relative to the plank. What is the speed of the plank relative to the pond now?

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6#
 
单选题 ( 1.0 分) 切至整卷模式 搜藏此题  
  97.18: A motorist travels 400 km at 80 km/h and 4r*/y .g1+cxw* mz vmzk00 km at 100 km/h. What is the average speed of thmk.+rg */y zmxwc z*v1e motorist on this trip?

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7#
 
单选题 ( 1.0 分) 切至整卷模式 搜藏此题  
  97.20: This question refers to the motion of a toyhnssfro6l67w/r 26maho jp+:m) .iu k car traveling along the x-axis. Thr k .ofor s:mpjn76ah/2h6+m6)lwu i se graph shown below is a plot of the car’s velocity in the x direction, $v_x$ versus time $t$.
During what time interval was the car moving towards its initial position at constant velocity?


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8#
 
单选题 ( 1.0 分) 切至整卷模式 搜藏此题  
  97.21: This question refers to the motion of a toy car traveling ara:wsxah6 15g long the x-axis. The graph shown below is a plot of the car’s vela5g16shax :wrocity in the x direction, $v_x$ versus time $t$.What was the acceleration at 33 s?


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9#
 
单选题 ( 1.0 分) 切至整卷模式 搜藏此题  
  97.22: This question refers to the motion of a toy car traveling along thapn0+c ,uz-t3cnzh,m e x-axis. The graph shown below is a plot of the ca,p +nt chnc-m3uza0z,r’s velocity in the x direction, $v_x$ versus time $t$.
How far did the car travel during the first 15 seconds?


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10#
 
单选题 ( 1.0 分) 切至整卷模式 搜藏此题  
  99.15: Given the graph of the velocity vs. time of a duck flying due south foa2vpvi (,nxlmpn8 1cuj7 *2phr the winter. At what point did the duck stop its forward motion? h2xn *2j cp7 v18(pnvua, lpim





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11#
 
单选题 ( 1.0 分) 切至整卷模式 搜藏此题  
  99.17: This question refer to the diagram below which shows the position fu8f-*z sw,r9l ;yv0brpx kja*i85nt and elapsed time of a car starting from rest and uniformly accelerating in a straight line. What was the average veloclrr;y-8t* f 50jkbpfn su8wxzi9,*a vity of the car during the third second?


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12#
 
单选题 ( 1.0 分) 切至整卷模式 搜藏此题  
  99.18: This question refer to tm zp o dmqf0wt (*sbi/+8vjs;*he diagram below which shows the position and elapsed time of a car starting from rest and uniformly accelerating in a straight line. The average accelefps/md**wiv0 ;s (mbj8oqt z+ration during the entire 3 second interval is closest to


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13#
 
单选题 ( 1.0 分) 切至整卷模式 搜藏此题  
  99.20: What is the shape of the velocif fhwacvtqc*2,guc*zw52gn2 -. d o( yty time graph for an object with the position time graph shown in the diagram at w uf.d(v-y cn,q2azhfw*5 *ogtc 2 cg2right?


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14#
 
单选题 ( 1.0 分) 切至整卷模式 搜藏此题  
  00.28: The following question refer to the followi 6 qjc.jray88hwcg 5t.ng information. An ideal elastic rubber ball is dropped fywj8jq5cg.t6hr 8.a c rom a height of about 2 meters, hits the floor and rebounds to its original height.
Which of the following graphs would best represent the distance above the floor versus time for the above bouncing ball?


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15#
 
单选题 ( 1.0 分) 切至整卷模式 搜藏此题  
  00.29: The following question refer to the followingwo;. 1ati7vk5tval -o information. An ideal elastic rubber ball is dropped from a height of about 2 meters, hits the floor and rebounds to its original height. ;towtva kl1 -5a7iv o.
Which of the following would best represent acceleration versus time for the bouncing ball?


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16#
 
单选题 ( 1.0 分) 切至整卷模式 搜藏此题  
  00.39: If a boat can travel with a spe+;zi.h n umnua8mv8;f3 rq.fqed of $v$ in still water, which of the following trips will take the least amount of time.

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17#
 
单选题 ( 1.0 分) 切至整卷模式 搜藏此题  
  01.01: The question refers to t1d jw9u6 dwp(lbsl8ez -d/e)r he following scenario: At $t_0$, two cars moving along a highway are side-by-side as they pass a third car stopped on the side of the road. At this moment the driver of the first car steps on the brakes while the driver of the stopped car begins to accelerate. The diagram below show the positions of each car for the next 5 seconds.
During which time interval would cars #2 and #3 be moving at the same average speed?


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18#
 
单选题 ( 1.0 分) 切至整卷模式 搜藏此题  
  01.02: The question refers to the following scenario: At zt31 5i.rd-:b oufmmo$t_0$, two cars moving along a highway are side-by-side as they pass a third car stopped on the side of the road. At this moment the driver of the first car steps on the brakes while the driver of the stopped car begins to accelerate. The diagram below show the positions of each car for the next 5 seconds.
About what position after $t_0$ would car #1 and car #2 have been side by side?


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19#
 
单选题 ( 1.0 分) 切至整卷模式 搜藏此题  
  01.03: The question refers to thea )tr21oy ktq92m*z 8r nbm1yq following scenario: At $t_0$, two cars moving along a highway are side-by-side as they pass a third car stopped on the side of the road. At this moment the driver of the first car steps on the brakes while the driver of the stopped car begins to accelerate. The diagram below show the positions of each car for the next 5 seconds.
Which of the three cars had the greatest average speed during these 5 seconds?


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20#
 
单选题 ( 1.0 分) 切至整卷模式 搜藏此题  
  01.04: The question refers to the followinp8pa ls hy k8); bz9)cqj+fpi3g scenario: At $t_0$, two cars moving along a highway are side-by-side as they pass a third car stopped on the side of the road. At this moment the driver of the first car steps on the brakes while the driver of the stopped car begins to accelerate. The diagram below show the positions of each car for the next 5 seconds.
If car #3 continues to constantly accelerate at the same rate what will be its position at the end of 6 seconds?


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21#
 
单选题 ( 1.0 分) 切至整卷模式 搜藏此题  
  01.33: A small ball rolls down a ramp, across a horizontal table top and of27 2dsh,gld1;la4rg(wzsh wxf the table edge. Which of the following would best represent a graph of the magnitude of tw;l2 2,rh1 zlhdwg(gs sxa47dhe ball's acceleration vs time?


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22#
 
单选题 ( 1.0 分) 切至整卷模式 搜藏此题  
  02.01: The graph represents the relationship between distance and time for an o q r8mt.nyc2ef:8m6nvbject t ey:.8mn vqc6r mnf82that is moving along a straight line. What is the instantaneous speed of the object at t = 5.0 seconds?


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23#
 
单选题 ( 1.0 分) 切至整卷模式 搜藏此题  
  02.02: The graph represents the relationship between distance and time 9 gb92cz fuibh6gpk51 for an object that is moving along a straight line. Between what times did the object have a non-zero accelerati1299 6b ug hbcgpk5zfion?


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24#
 
单选题 ( 1.0 分) 切至整卷模式 搜藏此题  
  10.07: A small object is thrown straightj5bf f2 +kyz4hajs :+fgg8p.e downward on Earth with an initial speed of 12.0 m/s from a position 10.0 j g+4e:kaf fjyfbh2 8sp5+.zgm above the ground. Ignoring air resistance, the speed of the object when it reaches the ground is

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25#
 
单选题 ( 1.0 分) 切至整卷模式 搜藏此题  
  02.11: The diagram below represents a toy cazkm ofs(ii .zrua6awpm f z5.)+1. ae;r starting from rest and uniformly accelerating across smw6zu 5ae;m f.aa(ifzk p z)1.io.+r the floor. The time and distance traveled from the start are shown in the diagram.
What was the average speed of the cart between 0.1 seconds and 0.3 seconds?


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26#
 
单选题 ( 1.0 分) 切至整卷模式 搜藏此题  
  02.12: The diagram below represe3jcrxbae.3 /z nts a toy car starting from rest and uniformly accel3 3b c/exr.ajzerating across the floor. The time and distance traveled from the start are shown in the diagram.
What was the acceleration of the cart during the first 0.4 seconds?


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27#
 
单选题 ( 1.0 分) 切至整卷模式 搜藏此题  
  02.13: The diagram below rdhq , 8y.cql:represents a toy car starting from rest and uniformly accelerating across the floor. The time and distance thdcqyl.q,r :8 raveled from the start are shown in the diagram.
What was the instantaneous velocity of the cart at 96 centimeters from the start?


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28#
 
单选题 ( 1.0 分) 切至整卷模式 搜藏此题  
  04.08: The diagram shows a u 4ny*7 6f eg0g-ivfzivniformly accelerating ball. The position of the ball each secondg i*6yg zvf-nv0 f47ie is indicated.
What is the average speed of the ball between 3 and 4 seconds?


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29#
 
单选题 ( 1.0 分) 切至整卷模式 搜藏此题  
  04.09: The diagram shows a uniformly accelerating ballsz1 4,5dyqwrzf l/q)t . The position of the ball each second is indicate )df/wrsz,1 q5yzl4qt d.
Which of the following is closest to the acceleration of the ball?


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30#
 
单选题 ( 1.0 分) 切至整卷模式 搜藏此题  
  02.17: The motion of a circus cc lk:9-vy4qbm lown on a unicycle moving in a straight line is shown in the graph below.cy94q l k-m:bv
What would be the acceleration of the clown at 5 s?


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31#
 
单选题 ( 1.0 分) 切至整卷模式 搜藏此题  
  02.18: The motion of a circus clown on a unicycle movingprqh) +-u4b jz in a straight line is shownr4 h+)bjzuqp- in the graph below.
After 12 seconds, how far is the clown from her original starting point?


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32#
 
单选题 ( 1.0 分) 切至整卷模式 搜藏此题  
  03.04: When an object falls fre .f 3eb*wu+raqely in a vacuum near the surface of the earth

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33#
 
单选题 ( 1.0 分) 切至整卷模式 搜藏此题  
  03.11: The accompanying graph describes the motion of a marble o xa,f;.2dhy(;qquk6 4wv rm ypn a table top for 10 second.mw( v4 fyr,q k h;6y;x2pdauqs. For which time interval(s) did the marble have a negative velocity?


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34#
 
单选题 ( 1.0 分) 切至整卷模式 搜藏此题  
  03.12: The accompanying graph describes the motion of bba c(vxrk6* 9a marble on a table top for 10 sec6r c* 9kxva(bbonds. For which time interval(s) did the marble have a positive acceleration?


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35#
 
单选题 ( 1.0 分) 切至整卷模式 搜藏此题  
  03.13: The accompanying graph describes the motion of a marb;d6 soud; qv5s3 ngx+d)ure)nle on a table top for 10 seconds. What is the marbles average acceleration betweeuug5x o3ndq dvre)ds+6n; ;s )n t = 3.3 s and t = 3.8 s


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36#
 
单选题 ( 1.0 分) 切至整卷模式 搜藏此题  
  03.20: A car accelerates un+j x7e el*o-kziformly from rest for a time of $2.00\;s$ through a distance of $4.00\;m$. What was the acceleration of the car?

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37#
 
单选题 ( 1.0 分) 切至整卷模式 搜藏此题  
  16.06: An object, thrown straight downwa tye .l wyxsi-03d9-ofrd with a speed of $20.0\;m/s$, takes $2.00\;s$ to reach the ground below. From what height above the ground was the object thrown? Ignore air resistance.

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38#
 
单选题 ( 1.0 分) 切至整卷模式 搜藏此题  
  04.03: Which of the following graphs x:s0znw p 5fc2could correctly represent the motion of an object moving with a n52wzfcs x:0pconstant speed in a straight line?


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39#
 
单选题 ( 1.0 分) 切至整卷模式 搜藏此题  
  03.24:The accompanying/5 ug-d;gcbfg graph describes the motion of a toy car across the floor for 10 seconds. What is the acceleration of the toy cb-fdggu c/ 5g;ar at t = 4 s?


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40#
 
单选题 ( 1.0 分) 切至整卷模式 搜藏此题  
  03.25:The accompanying graph describes the motion of a toy car um3prtz3v y /+vskv-++vbk n*across the floor for 10 seconds. What was the total displacement of the toy car for the entire 10 second intervmy r*/3vv tz+vk -nbku+ps 3+val shown?


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41#
 
单选题 ( 1.0 分) 切至整卷模式 搜藏此题  
  03.26:The accompanying graph describes the2ft .ik,:*hqjps j 9:vm lwu-i motion of a toy car across the floor for 10 seconds. At what times or time intervals must the net force on the toy car be zerjsvk:itlihp m2q*w j.9 -:fu ,o?


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42#
 
单选题 ( 1.0 分) 切至整卷模式 搜藏此题  
  16.03: A car accelerates uniformly from 0b6cqyz 1 af1) *nf*rne km/hr to 60 km/hr in 4.50 s. Which one of the follrb)n6cfna1 fyz1 q*e *owing choices best represents the acceleration of the car?

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43#
 
单选题 ( 1.0 分) 切至整卷模式 搜藏此题  
  06.07: A car has the velocityo)yhwm;r heox+,b,qyt)m (y: versus time curve shown. Which of the following statements regarding its motion i ,h)yowyer +() ,mo hbxtqm:;ys NOT CORRECT?


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44#
 
单选题 ( 1.0 分) 切至整卷模式 搜藏此题  
  07.17: A toy car moves along the x-axis according to the velocity versus time j1stz 11 :/cyvl oui3xcurve shown tos/1y1o xul 1jzitvc: 3 the right. When does the car have zero acceleration?


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45#
 
单选题 ( 1.0 分) 切至整卷模式 搜藏此题  
  06.22: During an interval of time, a tennis ball is moved so that the v8( jt 2sa2) otqa1nmbangle between the velocity and the acceleration of the ball is kept at a constant 120 degree. Which stabm2 atv)js on21a(t8 qtement is true about the tennis ball during this interval of time?

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46#
 
单选题 ( 1.0 分) 切至整卷模式 搜藏此题  
  07.03: Two automobiles are 150 kilometers apare w2ed5l v8jjp-xjy 0v2 d0gn+t and traveling toward each other.yg ejvx 8+pe02j-52 0jnwdldv
is moving at 60 km/h and the other is moving at 40 km/h. In how many hours will they meet?

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47#
 
单选题 ( 1.0 分) 切至整卷模式 搜藏此题  
  07.04: A particle moves on the x-axisn sme, nv1 bx;u z+bwd)h))xk2. When the acceleration is positive and increasinsd)be k, n) z hwv);xmxb2n1u+g

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48#
 
单选题 ( 1.0 分) 切至整卷模式 搜藏此题  
  07.12: The definition of averag4 sfup8borj;n oek(j3y6 n(r1 e velocity is

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49#
 
单选题 ( 1.0 分) 切至整卷模式 搜藏此题  
  16.18: For any motiondb14 8dd2;qj 3xnfpmd in two dimensions, which one of the following choices identifies quantities that mustj dqb8x d3;fm21pdd4n have the same direction?

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50#
 
单选题 ( 1.0 分) 切至整卷模式 搜藏此题  
  09.17: A toy car moveed(tlg dix87d/ 7pc7 ss $3.0\;m$ to the North in 1 second. The car then moves at $9.0\;m/s$ due South for 2 seconds. What is the average speed of the car for this three second trip?

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51#
 
单选题 ( 1.0 分) 切至整卷模式 搜藏此题  
  07.05: The position-tc vttq 0y:5c6n9l-z6 bl g2fyvime, $y\;vs\;t$, graph for the motion of an object is shown. What would be a reasonable equation for the acceleration that would account for this motion?


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52#
 
单选题 ( 1.0 分) 切至整卷模式 搜藏此题  
  09.31: A car moves to the right along a one-dimensional+d4qoc 7 sesx1 track for total time T in twos+4ox1cs7 deq parts.
• Part One: The car maintains constant non-zero speed V for the first $\frac{3}{4}$ of the total time.
• Part Two: The car accelerates uniformly to rest during the last $\frac{1}{4}$ of the total time.
What is the ratio of the distance traveled during Part One of the trip to the distance traveled during Part Two of the trip?

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53#
 
单选题 ( 1.0 分) 切至整卷模式 搜藏此题  
  08.23: The velocity vs. time graph for the motion of a car on a straigg -kw*xk1yy 9:qi3o hjht track is shown in the diagram. The thick line represents the velocik31 jx*y-gh oik9yw:qty. Assume that the car starts at origin $x=0$. At which time is the car the greatest distance from the origin?


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54#
 
单选题 ( 1.0 分) 切至整卷模式 搜藏此题  
  08.24: The velocity vs. time graph fot 283zjg ng7 b;au5s,qfa2lof hg(s* cr the motion of a car on a straight track is shown in the diagram. The thi,58zuj ggoftcl;hf g2*q32s( aab ns 7ck line represents the velocity. Assume that the car starts at origin $x=0$. What is the average speed of the car for the 10 second interval?


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55#
 
单选题 ( 1.0 分) 切至整卷模式 搜藏此题  
  09.08: Consider the motion of an object given by the-zfexke :8ak1h8icb gx 3z-0s position vs. time graph shown. For what time(s)b: zexze0ga8sh- ki-f1ckx38 is the speed of the object greatest?


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56#
 
单选题 ( 1.0 分) 切至整卷模式 搜藏此题  
  10.11: Consider the motion of an object given by the velocitb* 04akd) jsep 9nu3wgy vs. time graph shown. For which time(s) is the acceleration of the object equal to 0nap)* k9sw03 jb4ude g?


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57#
 
单选题 ( 1.0 分) 切至整卷模式 搜藏此题  
  10.24: By computing the area under the acceleration vs. time graphx6zf,(.vqood 8c(nvje;nk 2w for a fixed time interval of an object’s n;ocj2ex .6(wf vvn d(o ,zqk8motion, what quantity has been determined for that object?

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58#
 
单选题 ( 1.0 分) 切至整卷模式 搜藏此题  
  11.08: An object moves along a horizontal line with increasing spn)ih) e)bq ;ig j6(ucneed.
choices could represent the signs of the velocity and of the acceleration for the object to achieve this motion?

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59#
 
单选题 ( 1.0 分) 切至整卷模式 搜藏此题  
  11.14: A car makes a trip in two qf, f86rk+z56llao m7nyl (vtsw3 i5nparts:
Part 1: it travels a distance of 800 m at a constant speed of 4.0 m/s.
Part 2: it travels a distance of 1200 m at a constant speed of 20.0 m/s.
What is the average speed of the car for the entire two-part trip?

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60#
 
单选题 ( 1.0 分) 切至整卷模式 搜藏此题  
  13.02:A small object is released from rest and re9 yfbok/ e,rkryry2i7+ e 6y9waches the ground in a time of $2.50\;s$. Neglect air resistance. With what speed does the object reach the ground?

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61#
 
单选题 ( 1.0 分) 切至整卷模式 搜藏此题  
  13.03:A small object is released from rest and reaches *n e ouecw2q;4the ground in a time of $2.50\;s$. Neglect air resistance. From what height above the ground was the object released?

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62#
 
单选题 ( 1.0 分) 切至整卷模式 搜藏此题  
  13.17: A position vshd4/4 0p*gy f.iacipd . time graph of a particle moving along a horizontal axis is shown. What is the total distance trave0yg /c*ia4fp.ih pd4 dled by the particle from t=0 to t=10s ?


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63#
 
单选题 ( 1.0 分) 切至整卷模式 搜藏此题  
  13.18: Which one of the following choices correctly identifie07nse/ve3u)sep gf(h s all of the listed situations for which there is a nong epsnfe )h7 uv(s/03e-zero acceleration?
Situation I : A point object moves in a straight line with increasing speed.
Situation II : A point object moves in a circular path with constant speed.
Situation III: A point objects moves in a circular path with decreasing speed.

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64#
 
单选题 ( 1.0 分) 切至整卷模式 搜藏此题  
  13.32: An acceleration vs. time graph for an object moving along a line is shownw /:la3nsq 9;cglh*xf. The objehn f3 cl:g9qsx al/;*wct starts from rest at time t=0 s. At what time(s) does the object attain a maximum displacement from its starting position?


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65#
 
单选题 ( 1.0 分) 切至整卷模式 搜藏此题  
  15.17: An object starts at the origin and its ver8b1w6 nv-kj olocity along a line vs. time is graphed. Which one of the following choices best gives the proper interval(s) of time for which the object is k o8 -16rjbwvnmoving away from the origin?


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66#
 
单选题 ( 1.0 分) 切至整卷模式 搜藏此题  
  15.09: Two cars are moving to the right on a horizontal track, each with constanx9 + vsyj 4i ph4/0rh exqow22xkkc)q3t acceleration. At an instant of time, the infors9o xvh3i4+q)h jc 2rkpyq xwx e4k/02mation about the cars is shown:
Car #1: position = 125.0 m; velocity = 13.0 m/s; constant acceleration = $1.5\;m/s^2$
Car #2: position = 80.0 m; velocity = 9.30 m/s; constant acceleration = $5.5\;m/s^2$
During the next 1.0 second of motion, which one of the following choices best represents what happens to the distance between the cars?

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67#
 
单选题 ( 1.0 分) 切至整卷模式 搜藏此题  
  15.14: A particle has a pp 5yfz7 o w-xaq95x3 mbkc91mo)q,emcosition $x$, as a function of time $t$, given as $x(t) = -15 - 25t + 10t^2$. Which one of the following choices represents the magnitude of the particle’s acceleration? All quantities are expressed in base SI units.

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68#
 
单选题 ( 1.0 分) 切至整卷模式 搜藏此题  
  15.41: For the entire time shown in the graph, ;tuk,ns6( 0oq-x i tzqwhich one of the following choices correctly describes the ;ik-ntqt0 s( ,ouz qx6relationship between the average speed of the truck to that of the car?


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69#
 
单选题 ( 1.0 分) 切至整卷模式 搜藏此题  
  15.42: Which one of the following choices best describes the instants of tiz0k+,lnkr8 9l*k.fdfwydp g b 0d7:nv me, at which the car and trunk0 f.*kd,+:b p9g8 fdlk lynr07zwvdck travel with the same speed?

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70#
 
单选题 ( 1.0 分) 切至整卷模式 搜藏此题  
  17.30: Two cars P and Q, each start from rest at the origin and wz415-t g 0;uzbzuwu mdill move along the x-axis. The acceleration vs. time graph ;zwzb0u u ut15zdg4m- for each car is shown. Which one of the following choices correctly identifies the relationship for both the speeds $v$ and the positions $x$ of the cars at time T?


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71#
 
单选题 ( 1.0 分) 切至整卷模式 搜藏此题  
  16.02: The position vs. time graph of an object moving on a horizontal line is ah mi1wzy;a3+-f 8kfm shown. At what time(s) is the objecfkh1a;y+ zwmi 8 -mfa3t moving with its greatest speed?


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72#
 
单选题 ( 1.0 分) 切至整卷模式 搜藏此题  
  17.08: A mass moves along the x-axis following the position vs. time 1i o5nltj on0. gxh.rl nth0022phle6graph provided. During what time interval(s) does the mass have zer.ttoign1e 2l5j.2l0l n 0o xh60r pnhho acceleration?


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