What is the derivative of Acceleration with respect to time?
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Acceleration is the derivative of velocity with respect to time: a(t)=ddt(v(t))=d2dt2(x(t)). Momentum (usually denoted p) is mass times velocity, and force (F) is mass times acceleration, so the derivative of momentum is dpdt=ddt(mv)=mdvdt=ma=F.
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Acceleration is the derivative of velocity. Integrate acceleration to get velocity as a function of time. We've done this process before. We called the result the velocity-time relationship or the first equation of motion when acceleration was constant.
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