A Force is an influence that can change the motion of an object via a push or pull deriving from interaction with another object.
A field is a mathematical set of numbers for every point in space which can be operated on algebraically.
Thus Forces are thought to be the product of direct interaction between two objects, ultimately mediated by some fundamental particle. While fields are thought to represent a state or shape of the medium within which the objects are located.
For example, Newton’s Gravitational Force versus Einstein’s Gravitational Field.
Related
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Acceleration
Acceleration describes the rate of change of velocity with respect to time.
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Vector
A Vector is simply a quantity that has both a magnitude and a direction. In contrast, a scalar is a quantity that has a magnitude only.
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Velocity
Velocity tells you how fast an object is moving in a certain direction.