The position vector of a body, with respect to the origin, is given by \(r = 4ti + (12 - 3t)j\) at any time t seconds. (a) Find the velocity of the body ; (b) Calculate the magnitude of the displacement between t = 0 and t = 5.
Explanation
\(r = 4t i + (12 - 3t)j\) (a) \(v = \frac{\mathrm d r}{\mathrm d t} = 4i - 3j\) (b) When t = 0, r = 0i + 12j = 12j. When t = 5, r = 20i - 3j. Displacement = \(r_{t = 5} - r_{t = 0}\) = \(20i - 3j - 12j\) = \(20i - 15j\) \(|Disp| = \sqrt{20^{2} + 15^{2}} = \sqrt{400 + 225}\) = \(\sqrt{625} = 25m\)
