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6.4: Motion in which the Resistance is Proportional to the Square of the Speed

There are not really any new principles; it is just a matter of practice with slightly more difficult integrals. We assume that the resistive force per unit mass is \( k \dot{x}^{2}\) . Here, although \( k\) plays a somewhat similar role to the \( \gamma \) of Section 3, it is not exactly the same thing as \( \gamma\), and indeed it is not dimensionally the same as \( \gamma \). What are the dimensions, and the SI units, of \( k\)?