# 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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