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

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step-by-step explanation: