Differentiation
Velocity (\(v\)) is the rate of change of displacement (\(s\)), therefore:
\(v = \dfrac{ds}{dt}\)
Acceleration (\(a\)) is the rate fo change of velocity (\(v\)), therefore:
\(a = \dfrac{dv}{dt} = \dfrac{d^2s}{dt^2}\)
Integration
Integration is the reverse process to differentiation, therefore:
\(s = \displaystyle\int{v}~dt\)
\(v = \displaystyle\int{a}~dt\)
Calculus in kinematics for motion in a straight line
\(v = \dfrac{ds}{dt}\)
\(a = \dfrac{dv}{dt} = \dfrac{d^2s}{dt^2}\)
\(s = \displaystyle\int{v}~dt\)
\(v = \displaystyle\int{a}~dt\)
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