Motion with Variable Acceleration
Category : JEE Main & Advanced
(i) If acceleration is a function of time
\[a=f(t)\] then \[v=u+\int_{\,0}^{\,t}{f(t)\,dt}\]
and \[s=ut+\int_{0}^{t}{\left( \,\int{f(t)\,dt} \right)}\,dt\]
(ii) If acceleration is a function of distance
\[a=f(x)\] then \[{{v}^{2}}={{u}^{2}}+2\int_{\,{{x}_{0}}}^{\,x}{f(x)\,dx}\]
(iii) If acceleration is a function of velocity
\[a=f(\upsilon )\] then \[t=\int_{\,u}^{\,v}{\frac{dv}{f(v)}}\] and \[x={{x}_{0}}+\int_{\,u}^{\,v}{\,\frac{vdv}{f(v)}}\]
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