A particle of mass m is acted upon by a force F given by the empirical law F=R/(t²)v(t). If this law is to be tested experimentally by observing the motion starting from rest, the best way is to plot

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(1) log v(t) against 1/t. Idea: integrate the law, then look for the pair of variables that leaves a straight line. m(dv)/(dt)=R/(t²)v, and separating the variables, (dv)/v=R/m(dt)/(t²). Integrating both sides, ln v=-R/m·1/t+C. That is of the form y=mx+c with y=log v and x=1/t, so those are the axes that give a straight line — and its slope then measures R/m. The minus sign in front means the line slopes downward, which is also a useful check on the data.

A particle of mass m is acted upon by a force F given by the empirical law F=R/(t²)v(t). If this law is to be tested experimentally by observing the motion starting from rest, the best way is to plot

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