Engineering Mechanics - DynamicsChapter 12Problem 12-1A truck traveling along a straight road at speed v1, increases its speed to v2in time t. If itsacceleration is constant, determine the distance traveled.Given:v120kmhrv2120kmhrt15 sSolution:av2v10ta1.852ms2dv1t12at2.d291.67 mProblem 12-2A car starts from rest and reaches a speed vafter traveling a distance dalong a straight road.Determine its constant acceleration and the time of travel.Given:v80ftsd500 ftSolution:v22adav22da6.4fts2vtvat12.5 sProblem 12-3A baseball is thrown downward from a tower of height hwith an initial speed v0. Determinethe speed at which it hits the ground and the time of travel.Given:h50 ftg32.2fts2v018ftsSolution:vv022gh.v59.5fts1
Engineering Mechanics - DynamicsChapter 12tvv00gt1.29 s*Problem 12–4Starting from rest, a particle moving in a straight line has an acceleration of a= (bt+ c). Whatis the particle’s velocity at t1and what is its position at t2?Given:b2ms3c60ms2t16 st211 sSolution:a t( )btc.v t( )0tta t( )´µ¶dd t( )0ttv t( )´µ¶dv t1+ ,0msd t2+ ,80.7 mProblem 12-5Traveling with an initial speed v0a car accelerates at rate aalong a straight road. How long will ittake to reach a speed vf? Also, through what distance does the car travel during this time?Given:v070kmhra6000kmhr2vf120kmhrSolution:vfv0at.tvfv00at30 svf2v022as.svf2v0202as792 mProblem 12-6A freight train travels at vv01eb0t0+ ,wheret is the elapsed time. Determine the distancetraveled in time t1, and the acceleration at this time.2
Engineering Mechanics - DynamicsChapter 12v060ftsb1st13 sSolution:v t( )v01eb0t0+ ,a t( )tv t( )dddt( )0ttv t( )´µ¶ddt1+ ,123.0 fta t1+ ,2.99fts2Problem 12-7The position of a particle along a straight line is given by sp=at3+bt2+ct. Determine itsmaximum acceleration and maximum velocity during the time interval t0dtdtf.Given:a1fts3b90fts2c15ftst00 stf10 sSolution:spat3bt2.ct.vptspdd322.c.aptvpdd2tspdd262b.Since the acceleration is linear in time then the maximum will occur at the start or at the end.We check both possibilities.amaxmax 60b.6f2b./+ ,amax42fts2The maximum velocity can occur at the beginning, at the end, or where the acceleration is zero.We will check all three locations.tcrb03atcr3 s3Given:
Engineering Mechanics - DynamicsChapter 12vmaxmax 3at022bt0.c.3f22f.c./3cr22cr.c./+ ,vmax135fts*Problem 12-8From approximately what floor of a building must a car be dropped from an at-rest positionso that it reaches a speed vfwhen it hits the ground? Each floor is a distance hhigher than theone below it. (Note: You may want to remember this when traveling at speed vf)Given:vf55 mphh12 ftg32.2fts2Solution:acgvf202acs.Hvf22acH101.124 ftNumber of floorsNHeight of one floor h12ftNHhN8.427NceilN( )The car must be dropped from floor numberN9Problem 12–9
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