If R(t) Is the Position Vector of a Particle in the Plane

question 35

Multiple Choice

If r(t) is the position vector of a particle in the plane at time t, find the indicated vector.
-Find the acceleration vector.
$\mathbf { r } ( t ) = ( 8 \ln ( 9 \mathrm { t } ) ) \mathbf { i } + \left( 3 \mathrm { t } ^ { 3 } \right) \mathbf { j }$

• A) \(a = - \frac { 8 } { t ^ { 2 } } i + 18 t j\)
• B) \(a = \frac { 8 } { t ^ { 2 } } t ^ { - 2 } i + 18 t j\)
• C) \(a = \frac { 8 } { t } i + 9 t j\)
• D) \(\mathbf { a } = - \frac { 8 } { 9 } \mathrm { t } ^ { - 2 } \mathbf { i } + 18 \mathrm { t }\)

---

Definitions:

Preoperational

The stage in Jean Piaget's theory of cognitive development where children (aged 2 to 7) begin to engage in symbolic play and struggle with logic and taking the perspective of others.

Cognitive Development

Cognitive Development is the process by which a child learns to reason, solve problems, and gain knowledge through interaction with the world around them, as described in theories such as those by Piaget.

Piaget's Stages

A theory of cognitive development devised by Jean Piaget, which describes how children's understanding of the world changes through four stages of development.

Object Permanence

A cognitive development milestone in which an infant realizes that objects continue to exist even when they cannot be seen or heard.