Problem 1.36

A particle \(A\) moves in one direction along a given trajectory with a tangential acceleration \(w_{\tau}=a \tau,\) where \(a\) is a constant vector coinciding in direction with the \(x\) axis (Fig. 1.4\(),\) and \(\tau\) is a unit vector coinciding in direction with the velocity vector at a given point. Find how the velocity of the particle depends on \(x\) provided that its velocity is negligible at the point \(x=0\).