A survey drone is programmed to follow a path in a horizontal plane such that its position vector r\mathbf{r}r metres, at time t t\,t seconds, is given by
r=(2t2−13t3)i+(10−5t−32t2)j \mathbf{r} = \left(2t^2 - \frac{1}{3}t^3\right)\mathbf{i} + \left(10 - 5t - \frac{3}{2}t^2\right)\mathbf{j} r=(2t2−31t3)i+(10−5t−23t2)jrelative to a fixed origin.
Find the exact speed of the drone when t=3t = 3t=3.
An engineer suggests that the magnitude of the drone's acceleration will be zero at some time t>0t > 0t>0. Determine whether the engineer's claim is correct. Fully justify your answer.
