The position vector of a particle $P$ at a time $t$ seconds, where $t \ge 0$, is given by

Question

The position vector of a particle $P$ at a time $t$ seconds, where $t \ge 0$, is given by $\overrightarrow{OP} = \begin{pmatrix} 2 + 12t \ 5 - 5t \end{pmatrix}$. Write down the initial position vector of $P$. Find the speed of $P$. Determine whether $P$ passes through the point with position vector $\begin{pmatrix} 158 \ -48 \end{pmatrix}$.

Accepted Answer

(a) $\begin{pmatrix} 2 \ 5 \end{pmatrix}$ (b) $13$ m / s (c) $P$ does not pass through the point.

Vectors - Vector Kinematics

Vectors - Vector Kinematics