Question

I’m having trouble with this problem. Please help

Answer 1

The software rendering this question really butchered it... I think it's saying the displacement vector for the particle is

`\vec r(t) = \sin(t) \, \vec\imath + 4t^3 \, \vec\jmath + 5t \, \vec k`

Differentiate twice with respect to time
`t` to get the velocity and acceleration vectors, respectively:

`(d\vec r)/(dt) = \vec v(t) = \cos(t) \,\vec\imath + 12t^2 \,\vec\jmath + 5 \,\vec k`

`(d^2\vec r)/(dt^2) = (d\vec v)/(dt) = \vec a(t) = -\sin(t) \,\vec\imath + 24t \,\vec\jmath`

Then at
`t=3`, the acceleration of the particle is

`\vec a(3) = -\sin(3)\,\vec\imath + 72\,\vec\jmath`

which most closely resembles the first choice.