CALCULUSHigher Concepts of Mathematics3. Give the physical interpretation of the following equation relatingthe force, F, applied to an object, its mass m, its instantaneousvelocity v and time t.F_{m}dvdtThis equation includes the derivative dv/dt; the derivative of thevelocity with respect to time. It is the rate of change of velocitywith respect to time. The force applied to an object equals themass of the object multiplied by the rate of change of velocity withrespect to time.4. Give the physical interpretation of the following equation relatingthe accelerationa, the velocity v, and the time t.advdtThis equation includes the derivative dv/dt; the derivative of thevelocity with respect to time. It is a rate of change. Theacceleration equals the rate of change of velocity with respect totime.GraphicalUnderstandingofDerivativesA function expresses a relationship between two or more variables. For example, the distancetraveled by a moving body is a function of the body’s velocity and the elapsed time. When afunctional relationship is presented in graphical form, an important understanding of the meaningof derivatives can be developed.Figure 4 is a graph of the distance traveled by an object as a function of the elapsed time. Thefunctional relationship shown is given by the following equation:s = 40t(5-4)The instantaneous velocity v, which is the velocity at a given instant of time, equals thederivative of the distance traveled with respect to time, ds/dt. It is the rate of change of s withrespect to t.MA-05 Page 34 Rev. 0

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