Impulse J produced from time x to y is defined as the integral from x to ydt of the resultant force F over the period [x, y].
From Newton's second law, force is related to momentum p by
F = dp/dt
Therefore, impulse is defined as the integral from x to y of dp/dt times dt. As the time differentials cancel, this is just the integral from x to y of dp. This gives us Δp, the change in linear momentum from time x to y. This is often called the impulse-momentum theorem.
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