The Position Vector of a Particle Is R(t) $t = 0$

question 108

Multiple Choice

The position vector of a particle is r(t) . Find the requested vector.
-The velocity at $t = 0$ for $\mathbf { r } ( \mathrm { t } ) = \ln \left( \mathrm { t } ^ { 3 } - 3 \mathrm { t } ^ { 2 } + 4 \right) \mathbf { i } - \sqrt { 2 \mathrm { t } + 36 } \mathbf { j } - 5 \cos ( \mathrm { t } ) \mathbf { k }$

• A) \(\mathbf { v } ( 0 ) = \frac { 1 } { 4 } \mathbf { i } - \frac { 1 } { 6 } \mathrm { j }\)
• B) \(\mathbf { v } ( 0 ) = \frac { 1 } { 6 } \mathbf { j }\)
• C) \(\mathbf { v } ( 0 ) = - \frac { 1 } { 6 } \mathrm { j }\)
• D) \(\mathbf { v } ( 0 ) = \frac { 1 } { 4 } \mathbf { i } - \frac { 1 } { 12 } \mathbf { j } + 5 \mathbf { k }\)

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Definitions:

Slip

The difference between the synchronous speed of an induction motor's magnetic field and the actual speed of the rotor, expressed as a percentage.

Voltage

The electrical potential difference or force that causes current to flow in a circuit.

Magnetic Flux

Magnetic flux refers to the measure of the quantity of magnetism, considering the strength and the extent of a magnetic field.

Pole Polarity

Refers to the magnetic polarity (north or south) of the poles in a magnetic field, crucial in the functioning of electric motors and generators.