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Define coordinate systems for motion problems Recognize that the chosen coordinate system affects the sign of objects positions Define displacement Determine a time interval Use a motion diagram to answer questions about an object s position or displacement

Returning a Specific Fiscal Year The Year Before FY 2003 The Year After A Range of Dates Without a Range Operator Going Back in Time with ParallelPeriod Going Forward in Time with ParallelPeriod Too Far into the Future How Far into the Future How Far Back Range with OpeningPeriod and Null Range with ClosingPeriod and Null

ould it be possible to take measurements of distance and time from a motion diagram, such as the motion diagram of the runner Before taking the photographs, you could place a meterstick or a measuring tape on the ground along the path of the runner The measuring tape would tell you where the runner was in each image A stopwatch or clock within the view of the camera could tell the time But where should you place the end of the measuring tape When should you start the stopwatch

It is standard practice for engineers to design small gaps, called expansion joints, into concrete-and-steel highway bridges to allow for the expansion of parts in the heat of summer Objects expand only a small amount when they are heated, but that small amount could be several centimeters in a 100-m-long bridge If expansion gaps were not present, the bridge could buckle or parts of it could break High temperatures can also damage railroad tracks that are laid without expansion joints, as shown in Figure 13-20 Some materials, such as the ovenproof glass that is used for cooking and laboratory experiments, are designed to have the least possible thermal expansion Large telescope mirrors are made of a ceramic material that is designed to undergo essentially no thermal expansion To understand the expansion of heated solids, picture a solid as a collection of particles connected by springs that represent the attractive forces between the particles When the particles get too close, the springs push them apart When a solid is heated, the kinetic energy of the particles increases, and they vibrate rapidly and move farther apart, weakening the

attractive forces between the particles As a result, when the particles vibrate more violently with increased temperature, their average separation increases and the solid expands The change in length of a solid is proportional to the change in temperature, as shown in Figure 13-21 A solid will expand in length twice as much when its temperature is increased by 20 C than when it is increased by 10 C The expansion also is proportional to its length A 2-m bar will expand twice as much as a 1-m bar with the same change in temperature The length, L2, of a solid at temperature T2 can be found with the following equation, where L1 is the length at temperature T1 and alpha, , is the coefficient of linear expansion L2 L2 L1 L1 L Coefficient of Linear Expansion L1(T2 L1(T2 L1 T