Use the given acceleration vector to find the velocity and position vectors. then find the position at time t=2: a(t) = −32k, v(0) = 3i − 2j + k, r(0) = 5j + 2k

the velocity and position vector is given by;

v(t) = 3i + 2j + (1-32t)k

r(t) = (3t)i + (5-2t)j + (2+t-16t^2)k

The position at time t=2; r(2)

r(2) = 6i + j - 60k

Step-by-step explanation:

Shown in the attachment.

The velocity vector is and the position vector is

When t = 2  the position is

Step-by-step explanation:

To find the position function, you should integrate twice, each time using one of the initial conditions to solve for the constant of integration. The velocity vector is

where .

Letting t = 0 and applying the initial condition

Therefore,

So, the velocity at any time t is

Integrating once more produces

Letting t = 0 and applying the initial condition

Therefore,

The position vector is

When t = 2  the position is

answer: city needs 2.4 inches of rainfall more to match the record of 40 inches.

step-by-step explanation:

since we have given that

total annual rainfall a city record = 40 inches

this year, total rainfall recorded = 37.6 inches

number of inches of rainfall   is needed to match the record of 40 inches is given by

hence, city needs 2.4 inches of rainfall more to match the record of 40 inches.

not sure but it may be b, as i said i'm not sure.