Infinite string at rest for t<0, has instantaneous transverse blow at t=0 which gives initial velocity of for a constant V. Derive the position of string for later time.

I thought that this would be with , and . So use the d'Alembert solution . Then applying these gets the forms of f, g.

Is this correct? I am a bit nervous because I am self-teaching some of this wave equation stuff and I am not good at applying the theory to a practical question