A small package is released from rest at A andmoves along the skate wheel conveyor ABCD.The package has a uniform acceleration of4.8 mls2 as it moves down sections AB and CD,and its velocity is constant between Band C. Ifthe velocity of the package at D is 7.2 mis,determine (a) the distance d between C and D,(b) the time required for the package to reach D.

SOLUTION

(a) For A~B

and C~D

we have v2 =v5 +2a(x-xo)

Then,

atB v~c = 0 + 2(4.8 mls2)(3 - 0) m

= 28.8 m2/s2 (vBC = 5.3666 mls)

and atD 2 2 d=Xd -xcvD = vBC + 2aCD(xD - xc)

,t or (7.2 mlS)2 =(28.8 m2/s2)+2(4.8 mls2)d

or d = 2.40 m .••••

(b) For A~B

and C~D,

we have v=vo +at

Then A~B

5.3666 mls=0+(4.8 mlS2)tAB

or tAB = 1.11804 s

and C~D 7.2 mls=5.3666 mls+(4.8 mlS2)tCD

or tCD =0.38196 S

PROPRIETARY MATERIAL. © 2009 The McGraw-Hill Companies, Inc. All rights reserved. No part of this Manual may be displayed,reproduced or distributed in any form or by any means, without the prior written permission of the publisher, or used beyond the limiteddistribution to teachers and educators permitted by AfcGraw-Hillfor their individual course preparation. If you are a student using this Manual,you are using it without permission.

pt-. ----------------------~

PROPRIETARY MATERIAL. © 2009 The McGraw-Hill Companies, Inc. All rights reserved. No part of this Manual may be displayed,reproduced or distributed in any form or by any means, without the prior written permission of the publisher, or used beyond the limiteddistribution to teachers and educators permitted by McGraw-Hillfor their indivtdual course preparation. If you are a student using this Manual,you are using it without permission.

A police officer in a patrol car parked in a 70 km/h speed zone obsem:s a passing automobik traveling at aslow, constant speed. Believing that the driver of the automobile might be intoxicated, the officer starts hiscar. accelerates uniformly to 90 km/h in 8 s, and, maintaining a constant velocity of 90 km/h, overtakes themotorist 42 s after the automobile passed him. Knowing that 18 s elapsed before the officer began pursuingthe motorist, dl~termine (a) the distance the officer traveled before overtaking the motorist, (b) the motorist'sspet:d.

,_._--------------------------------- ----~-----------_. __ ._.-

I SOLUTIONI

I

(a) Patrol car:

for 18 s < t ::.s 26 s:

Xp

::::0+O(t-18)-..!..ap(t -18)2

2

(Xp )42 = 100 m + (25 m/s)(42 - 26)s

=500m

PROPRIET4RY ilJATERlAL. ,!] 2009 The McGraw-Hill Companies. Inc. All rights reserved. Yo part ot this Manual Inuy be di,p/ayt:d.reproduced or distribuTed in (lny fbrm or by any means, without the prior lv/"itlen permission oj" ilk publisher, 0/' used lvyonri tIle tinnlcddistribution to teachers and educators permitted by McGraw-Hill/or their individual COllI'S';; preparation. {(VOl! ore a student using this A!miUul.you are using it without perm is.,ion.

In a boat race, boat A is leading boat B by 120 ftand both boats are traveling at a constant speedof 105 mi/h. At t = 0, the boats accelerate atconstant rates. Knowing that when B passes A,t = 8 s and vA = 135 milh, determine (a) theacceleration of A, (b) the acceleration of B.

(VA)O = 105 mi/h = 154 ft/s

VA = 135 milh = 198 ft/s

198 ft/s=154 ft/s+aA(8s)

120 ft+(l54 ftls)(8s) +.l(5.50 ft/s2)(8s)22

1= (154 ft/s)(8 s) + -aB(8 S)22

PROPRIETARY MATERIAL.© 2009 The McGraw-Hill Companies, Inc. All rights reserved. No part of this Manual may be displayed,reproduced or distributed in any form or by any means, without the prior wrillen permission of the publisher, or used beyond the limiteddistribution to teachers and educators permilled by McGraw-Hili for their individual course preparation. If you are a student using this Manual,you are using it without permission.

Two automobiles A and B are approachingeach other in adjacent highway lanes. Att = 0, A and Bare 1 km apart, their speedsare VA == 108 km/h and VB == 63 kmJh, andthey are at Points P and Q, respectively.Knowing that A passes Point Q 40 s after Bwas there and that B passes Point P 42 safter A was there, determine (a) theuniform accelerations of A and B, (b) whenthe vehicles pass each other, (c) the speedof B at that time.

1000 m == (30 m/s)(40 s)+~a4(40 S)22 .

11000 m == (17.5 m/s)(42 s) +-aB(42 S)22

0.05045t~B + 95t3B - 2000 = 0

t = 20.822 sand t = -1904 s

t>O~tw ~20.8~~jPROPRIETARY MATERIAL. ((;1 2009 The McGraw-Hill Companies, Inc. All rights reserved. No part of this A/anual may be di;played,reproduced or distributed in any.form or by any means, without the prior written permission of the publisher, or used beyond the limiteddistribution to teachers and educators permitted by McGraw-Hill.for their individual course preparation. If you are a student using this AJanllal,you are using it without permission.

VB = 17.5 m1s + (0.30045 m1s2)(20.822 s)

=23.756 m1s

PROPRIETARY MATERIAL. © 2009 The McGraw-Hill Companies, Inc. All rights reserved. No part of this Manual may be displayed,reproduced or distributed in any form or by any means, without the prior written permission of the publisher, or used beyond the limiteddistribution to teachers and educators permitted by McGraw-Hill for their individual course preparation. If you are a student using this Manual,you are using it without permission.

Two blocks A and B are placed on an incline as shown. Att = 0, A is projected up the incline with an initial velocityof 27 fils and B is released from rest. The blocks pass eachother 1 s later, and B reaches the bottom of the inclinewhen t = 3.4 s. Knowing that the maximum distance fromthe bottom of the incline reached by block A is 21 fi andthat the accelerations of A and B (due to gravity andfriction) are constant and are directed down the incline,determine (a) the accelerations of A and B, (b) the distance d,(c) the speed of A when the blocks pass each other.

1 2XB =O+Ot+-aBt

2

At t=3.4 s,xB =d:

Thus (XA)I + (XB)I = (xBh4

[(27 ft/s)(l S)+~(-17.3571 fi/s2)(1 S)2]

[1 ~] 1 ry

+ '2aB(l st ='2aB(3.4 st

PROPRIETARY MATERIAL. 'g 2009 The McGraw-Hill Companies, Inc. All rights reserved. No part of this Iv[anual may be displayed,reproduced or distributed in any form or by any means, without the prior written permission of the publisher, or used beyond the limiteddistribution to teachers and educators permitted by McGraw-Hillfor their individual course preparation. Ijyou are a student using this Manual,you are using it without permission.

rI1!

PROPRIETARY MATERIAL. © 2009 The McGraw-Hill Companies, Inc. All rights reserved. No part of this Manual may be displayed,reproduced or distributed in any form or by any means, without the prior written permission of the publisher, or used beyond the limiteddistribution to teachers and educators permitted by McGraw-Hill/or their individual course preparation. If you are a student using this Manual,you are using it without permission.