What's the difference between $v = a\cdot t$ and $\vec{v} = \int \vec{a} \, \mathrm dt$

The formula $v = v_0 + at$ assumes that the acceleration is constant. The formula $v = v_0 + \int_{t_0}^{t_f} a(t) \, dt$ allows for the possibility that the acceleration changes with time.


The first formula $v=at$ is valid for a constant whereas the second one is valid also for not constant acceleration that is $v=\int_0^t a(u)du$.

Tags:

Calculus

Mathematical Physics

Vector Fields

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