Movement and position

A drone $P\,$ moves in a horizontal plane. At time $t\,$ seconds ( $\ge 0$ ), the velocity of $P$ , $s−1\mathbf{v}\text{ m s}^{-1}$ , is given by

\mathbf{v} = (3t^2 - 6t)\mathbf{i} + (4t - 3)\mathbf{j}

At time $t = 0$ , the position vector of $P\,$ relative to a fixed origin $O\,$ is $m(5\mathbf{i} - 2\mathbf{j})\text{ m}$ .

Find the position vector of $P\,$ at the instant when its acceleration is parallel to the vector $3i+2j3\mathbf{i} + 2\mathbf{j}$ .

$i\mathbf{i}$

$−4i+2j-4\mathbf{i} + 2\mathbf{j}$

$5j5\mathbf{j}$

$6i+4j6\mathbf{i} + 4\mathbf{j}$

Movement and position Questions

A drone $P\,$ moves in a horizontal plane. At time $t\,$ seconds ( $\ge 0$ ), the velocity of $P$ , $s−1\mathbf{v}\text{ m s}^{-1}$ , is given by

\mathbf{v} = (3t^2 - 6t)\mathbf{i} + (4t - 3)\mathbf{j}

At time $t = 0$ , the position vector of $P\,$ relative to a fixed origin $O\,$ is $m(5\mathbf{i} - 2\mathbf{j})\text{ m}$ .

Find the position vector of $P\,$ at the instant when its acceleration is parallel to the vector $3i+2j3\mathbf{i} + 2\mathbf{j}$ .

$i\mathbf{i}$

$−4i+2j-4\mathbf{i} + 2\mathbf{j}$

$5j5\mathbf{j}$

$6i+4j6\mathbf{i} + 4\mathbf{j}$