An ion is being manipulated within a mass spectrometer. At time ttt seconds, the acceleration of the ion, a m s−2\mathbf{a} \text{ m s}^{-2}a m s−2, is modeled by the vector function:
a=(12kt2−6kt+5)i+(24t−10)j \mathbf{a} = (12kt^2 - 6kt + 5)\mathbf{i} + (24t - 10)\mathbf{j} a=(12kt2−6kt+5)i+(24t−10)jwhere kkk is a constant.
The initial velocity of the ion is (8i+3j) m s−1(8\mathbf{i} + 3\mathbf{j}) \text{ m s}^{-1}(8i+3j) m s−1.
At t=2t = 2t=2, the velocity of the ion is (48i+31j) m s−1(48\mathbf{i} + 31\mathbf{j}) \text{ m s}^{-1}(48i+31j) m s−1.
Show that k=1.5k = 1.5k=1.5.
