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Newton wrote that force is equal to the rate of change of momentum. This is

F = dp/dt (1). As momentum, p, is the product of mass, m, and velocity, v,

(1) is equivalent to F = dmv/dt (2). Velocity is the rate of change of position,

and becomes acceleration under differentiation with respect to time. Applying

the product rule to (2) gives F = vdm/dt + mdv/dt. Unless a body's mass is

changing (e.g. ejecting fuel to take off, or moving at relativistic speeds),

dm/dt = 0. So (2) becomes F= mdv/dt. But dv/dt is the acceleration, a.

So we can see that F = ma.

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