JEE Main & Advanced Physics Motion In One Dimesion Motion with Variable Acceleration

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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