We are given the speed of the train as a function of time, which is the rate of change of its position: \[\begin{aligned} v(t)=\frac{dx}{dt}\end{aligned}\] We need to find how its position, \(x(t)\), ...We are given the speed of the train as a function of time, which is the rate of change of its position: \[\begin{aligned} v(t)=\frac{dx}{dt}\end{aligned}\] We need to find how its position, \(x(t)\), changes with time, given the speed.