What force is required so that a particle of mass $m$ has the following position function?.
$$r ( t ) = 5 t ^ { 3 } \mathbf { i } + 10 t ^ { 2 } \mathbf { j } + 7 t ^ { 3 } \mathbf { k }$$
A) $\mathrm { F } ( t ) = 30 m t \mathbf { i } + 20 m \mathbf { j } + 42 m t \mathbf { k }$
B) $\mathrm { F } ( t ) = 30 m t ^ { 2 } \mathbf { i } + 20 m \mathbf { j } + 42 m t \mathbf { k }$
C) $\mathrm { F } ( t ) = 42 m t \mathbf { i } + 42 m \mathbf { j } + 20 m t \mathbf { k }$
D) $\mathrm { F } ( t ) = m t ^ { 2 } \mathbf { i } + 5 m t \mathbf { j } + 10 m t ^ { 2 } \mathbf { k }$
E) $\mathrm { F } ( t ) = 30 m t \mathbf { i } + 20 m \mathbf { j } + t \mathbf { k }$

Question

Quizplus · Accepted Answer

The force is given by the second derivative of the position function with respect to time, multiplied by the mass.$$\mathrm { F } ( t ) = m \frac { d ^ { 2 } \mathbf { r } ( t ) } { d t ^ { 2 } } = m \left( 30 t \mathbf { i } + 20 \mathbf { j } + 42 t \mathbf { k } \right) = 30 m t \mathbf { i } + 20 m \mathbf { j } + 42 m t \mathbf { k }$$

What Force Is Required So That a Particle of Mass mmm

What Force Is Required So That a Particle of Mass $m$