Write dawn the relationship between acceleration, initial velocity and final velocity.
By definition, the acceleration is (bold letters denote vectors):
where "\\mathbf{v}" is the instantaneous velocity, and "t" is the time. Thus, to find the final velocity at some moment of time one should integrate acceleration with respect to "t":
where "\\mathbf{v}_f" is the final velocity, "\\mathbf{v}_0" is the initial velocity, "t_0, t" are initial and final moments of time respectively.
Answer. "\\mathbf{v}_f = \\mathbf{v}_0 + \\int_{t_0}^t\\mathbf{a}dt".
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