A space probe far from the Earth is traveling at \(14.8\,\text{km/s}\). It has mass \(1312\,\text{kg}\). The probe fires its rockets to give a constant thrust of \(156\,\text{kN}\) for \(220\) seconds. It accelerates in the same direction as its initial velocity. In this time it burns \(150\,\text{kg}\) of fuel. Calculate the final speed of the space probe in \(\text{km/s}\).

Note: This is a bonus question. Skip if you haven't yet taken calculus.