Meriam, Kraige & Bolton — Kinematics of Particles: Problem 2_113

2/113 A particle moving along a plane curve has a position vector \(\mathbf{r}\), a velocity \(\mathbf{v}\), and an acceleration \(\mathbf{a}\). Unit vectors in the \(r\)- and \(\theta\)-directions are \(\mathbf{e}_r\) and \(\mathbf{e}_\theta\), respectively, and both \(r\) and \(\theta\) are changing with time. Explain why each of the following statements is correctly marked as an inequality. \[ \begin{array}{l l l} \dot{r} \neq v & \ddot{r} \neq a & \dot{\mathbf{r}} \neq \dot{r}\mathbf{e}_r \\ \dot{r} \neq v & \ddot{r} \neq a & \ddot{\mathbf{r}} \neq \ddot{r}\mathbf{e}_r \\ \dot{r} \neq \mathbf{v} & \ddot{r} \neq \mathbf{a} & \dot{\mathbf{r}} \neq r\dot{\theta}\mathbf{e}_\theta \end{array} \]