Integrate the equation dx / dt = -gt + gt0 + v0 in the paragraph after Eq. (1.11) to find x as a function of time. Use the condition that the particle was at x0 at time t0 to evaluate the integration constant and show that x = x0 - 1/2 g(t - t0)2 + v0(t - t0).
In Eq. 1.11

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g(t, ci C2 dt