Movement and position

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

\mathbf{v} = (3t^2 - 4t + 5)\mathbf{i} + (6t^2 - 12t - 2)\mathbf{j}

At time $t = 0$ , the position vector of $P\,$ relative to a fixed origin $O\,$ is $m(\mathbf{i} + 10\mathbf{j})\text{ m}$ .

Find the position vector of $P\,$ at the instant when its acceleration is parallel to the vector $2i+3j2\mathbf{i} + 3\mathbf{j}$ .

$m(10\mathbf{i} - 12\mathbf{j})\text{ m}$

$m(11\mathbf{i} - 2\mathbf{j})\text{ m}$

$m(5\mathbf{i} + 4\mathbf{j})\text{ m}$

$m(11\mathbf{i} + 6\mathbf{j})\text{ m}$

Movement and position Questions

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

\mathbf{v} = (3t^2 - 4t + 5)\mathbf{i} + (6t^2 - 12t - 2)\mathbf{j}

At time $t = 0$ , the position vector of $P\,$ relative to a fixed origin $O\,$ is $m(\mathbf{i} + 10\mathbf{j})\text{ m}$ .

Find the position vector of $P\,$ at the instant when its acceleration is parallel to the vector $2i+3j2\mathbf{i} + 3\mathbf{j}$ .

$m(10\mathbf{i} - 12\mathbf{j})\text{ m}$

$m(11\mathbf{i} - 2\mathbf{j})\text{ m}$

$m(5\mathbf{i} + 4\mathbf{j})\text{ m}$

$m(11\mathbf{i} + 6\mathbf{j})\text{ m}$