A 60-lb block is connected by an inextensible cable through the pulley to the fixed surface, as shown in Figure P1.12. A \(40 \mathrm{lb}\) weight is attached to the pulley, which is free to move vertically. A force of magnitude \(P=100\left(1+e^{-t}\right) \mathrm{lb}\) tows the block. The system is released from rest at \(t=0\).

(a) What is the acceleration of the \(60 \mathrm{lb}\) block as a function of time?

(b) How far does the block travel up the incline before it reaches a velocity of \(2 \mathrm{ft} / \mathrm{s}\) ?

40 lb FIGURE P1.12 60 lb 45 4=0.3 P