Final answer:
The acceleration field from the velocity field V = kx i - ky j is obtained by differentiating the velocity components with respect to time, resulting in A = dkx/dt i - dky/dt j. If position coordinates x and y are constants, the acceleration components are zero.
Step-by-step explanation:
To obtain the acceleration field from a given velocity field, one should take the time derivative of the velocity vector. The provided velocity field is V = kx i - ky j, where k is a constant, and x and y are the position coordinates in meters. Since no time dependency is explicitly given, we can assume x and y might be functions of time, so we are actually differentiating x(t) and y(t) with respect to time. For a constant k, the acceleration field is A = dkx/dt i - dky/dt j. If x and y are not functions of time (but constant values), then the acceleration components would be zero because the derivatives would be zero.
Since the velocity does not depend explicitly on time, if x and y are constant, then the acceleration field is zero. However, if the position coordinates x and y are time-dependent, we would need the functions x(t) and y(t) to actually determine the acceleration field.