Force is defined as the rate of change of momentum. Momentum is the product of mass and velocity. Mass is a constant for a given object at this level. So force is the product of the mass and the rate of change of velocity – and rate of change of velocity is known as acceleration.
All of this stuff gets much easier when you can use calculus: a lot of the formulas to memorise in mechanics are just special cases of standard results from calculus.
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