74Chapt. 6Newton’s Laws and Dynamics IIc) The second law with the forces written explicitly is a differential equation for velocity asfunction of variable time.A differential equation being an equation for a function thatcontains derivatives of various orders of the function. To solve a differential equation is tofind the function as an explicit function of the variable.Many, many physical problemscome down to solving differential equations. In this case, verify thatv=v0e−Ct+FlocoCm(1−e−Ct)is the explicit solution of the differential equation:v0is an initial velocity at time zero.What is the differential equation and solution ifFloco= 0?006 qfull 00740 3 3 0 tough math: quadratic drag force12. The quadratic drag force magnitude on a body isFdrag=bv2=12CρAv2,whereCis the dimensionless drag coefficient (which is typically in the range 0.4 to 1 [HRW-104]and is set by all kinds of things like shape and texture of the body),ρis fluid density,Ais thearea of body perpendicular to the flow (i.e., the cross sectional area), and
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