1. The gure below illustrates the automatic breaking control of a train, where U,(s)=L[u,(t)], V(s)=L[v(t)], u, is the input voltage representing a desired train speed, and v is the actual train speed,. The amplifier gain is K: 100, and the tachometer (velocity sensor) constant is K9=D.15. a. (10 points.) Suppose that the braking action can be modeled by a transfer function of the form F C s = E ((55)) = s + a , where 155(5): L[ea(t)], F (s): L[f(t)], 25m is the braking input and t) is the resulting B braking force. If t)=100(1-e"') is measured with eg=u(t) (the unit step function), determine the constants c and C. b. (10 points.) The train has mass M=5>