A search-and-rescue drone is deployed to locate a radio signal. At time ttt seconds, its position vector r\mathbf{r}r metres, relative to a fixed base station, is given by
[r=(23t3−5t2+12)i+(20t−2t2−7)j [\mathbf{r} = \left(\frac{2}{3}t^3 - 5t^2 + 12\right)\mathbf{i} + (20t - 2t^2 - 7)\mathbf{j} [r=(32t3−5t2+12)i+(20t−2t2−7)jCalculate the exact speed of the drone when t=4t = 4t=4.
An analyst suggests that the magnitude of the drone's acceleration will never fall to zero. Determine, with full justification, whether the analyst is correct.
