More than 2 300 years ago, the Greek teacher Aristotlewrote the first book called

Chapter 8, Problem 60

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More than 2 300 years ago, the Greek teacher Aristotlewrote the first book called Physics. Put into moreprecise terminology, this passage is from the end of itsSection Eta:Let P be the power of an agent causing motion;w, the load moved; d, the distance covered; andDt, the time interval required. Then (1) a powerequal to P will in an interval of time equal to Dtmove w/2 a distance 2d; or (2) it will move w/2the given distance d in the time interval Dt/2.Also, if (3) the given power P moves the given load w a distance d/2 in time interval Dt/2, then(4) P/2 will move w/2 the given distance d in thegiven time interval Dt.(a) Show that Aristotles proportions are included inthe equation P Dt 5 bwd, where b is a proportionalityconstant. (b) Show that our theory of motion includesthis part of Aristotles theory as one special case. Inparticular, describe a situation in which it is true,derive the equation representing Aristotles proportions,and determine the proportionality constant.