(a) Repeat Prob. 11.19, but this time let the external force be a Dirac delta function: F(t) = kS(t) (for some constant k). 17 [Note that the acceleration is now discontinuous at t = 0 (though the velocity must still be continuous); use the method of Prob. 11.19 

(a) To show that ∆a = – k/mτ. In this problem there are only two intervals to consider: (i) t < 0, and (ii) t > 0.] 

(b) As in Prob. 11.27, check that energy is conserved in this process.