A cart rolls up an inclined track

PHYSICS · Multi-part · Fermi University Physics · Scientific Practice & Experimental Methods · Mathematical Methods for Physics · Calculus of change and accumulation

Mathematical Methods for Physics, Ch The derivative as a physical instrument

Problem

A cart rolls up an inclined track, slowing as it climbs, past photogates set

0.20\,\mathrm{m}

apart, numbered from gate 5 to gate 7. A timer reads out the instant the cart's flag crosses each gate, each reading good to

\pm0.005\,\mathrm{s}

. Data: gate 5 at

0.84\,\mathrm{s}

, gate 6 at

1.02\,\mathrm{s}

, gate 7 at

1.22\,\mathrm{s}

. ((a)) Estimate the cart's speed at gate 6 using the forward difference (gates 6 and 7), the backward difference (gates 5 and 6), and the central difference (gates 5 and 7). ((b)) State the resolution error of the central-difference estimate, given the timer's reading error, and hence give the average speed from gate 5 to gate 7 with its timing uncertainty. What does that uncertainty leave out, if the average is used as the speed at gate 6?

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