A car's speed is measured by radar as

PHYSICS · Multi-part · Fermi University Physics · Scientific Practice & Experimental Methods · Mathematical Methods for Physics · Uncertainty in measurement

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

Problem

A car's speed is measured by radar as v=24.0 m s−1v = 24.0\,\mathrm{m\,s^{-1}}, with an uncertainty δv=0.3 m s−1\delta v = 0.3\,\mathrm{m\,s^{-1}}. Its kinetic energy is E=12mv2E = \tfrac12 m v^2 for a mass mm that is known exactly. ((a)) Use the differential dE=E′(v) dv\mathrm{d}E = E'(v)\,\mathrm{d}v to write the fractional error δE/E\delta E/E in terms of the fractional error δv/v\delta v/v. ((b)) Evaluate δE/E\delta E/E as a percentage for the data given. ((c)) If m=1200 kgm = 1200\,\mathrm{kg}, give EE and its absolute uncertainty δE\delta E, both to the precision the data support.

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