The equation r(t)= (3t+9)i+(sqrt(2)t)j+(t^2)k is the position of a particle in space at time t. Find the angle between the velocity and acceleration vectors at time t=0
What is the angle? radians

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Step-by-step explanation:

The velocity vector is found by deriving the position vector depending on the time:

In turn, acceleration vector is found by deriving the velocity vector depending on time:

Velocity and acceleration vectors at are:

Norms of both vectors are, respectively:

The angle between both vectors is determined by using the following characteristic of a Dot Product:

Given that cosine has a periodicity of . There is a family of solutions with the form:

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step-by-step explanation: