Final answer:
The three rectangular components of acceleration are found by taking the derivatives of the velocity components with respect to time. The x-component of acceleration is x, the y-component is y, and the z-component is 6yz² + x.
Step-by-step explanation:
The acceleration in a flow field is obtained by taking the partial derivatives of the velocity components with respect to time. In this case, the velocity equation is given as V = 3yz²j + xzj + yk.
To find the expressions for the three rectangular components of acceleration, we need to differentiate each component of velocity with respect to time.
The x-component of acceleration (ax) will be equal to the derivative of the x-component of velocity (Vx) with respect to time, and so on for the y-component (ay) and z-component (az).
Taking the derivatives of the velocity components, we get:
ax = x
ay = y
az = 6yz² + x