Suppose an object initially at \(x_{\mathrm{i}}\) at \(t_{\mathrm{i}}=0\) has a constant acceleration whose \(x\) component is \(a_{x}\). Use calculus to show that the \(x\) component of the velocity and the \(x\) coordinate at some final instant \(t_{\mathrm{f}}\) are given by Eq. 3.10 and Eq. 3.9, respectively,

Data from Eq. 3.9

Data from Eq. 3.10

x = x+x+at (constant acceleration)