Beach on the highway

A cart loaded with sand moves along a flat, straight track due to a constant force \(F\) parallel to the cart's velocity vector. The sand spills through a hole in the bottom at a constant rate \(z\) kg/s .

Find the time when the velocity of the cart will be \(\frac{F}{z}\) given that velocity of cart at \(t=0\) is zero, and the initial mass of the cart \(t=0\) is \(M\).

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