Physics KINEMATICS

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KINEMATICS

Motion with Variable Acceleration

(i) `(dv)/(dt)=a` `=>` `int_(v_1)^(v_2)dv=int_(t_1)^(t_2)adt`

(ii) `(dx)/(dt)=v` `=>` `int_(x_1)^(x_2)dv=int_(t_1)^(t_2)vdt`

(iii) `a=(dv)/(dt)=(dv)/(dx) . (dx)/(dt)` (By chain rule)

`:.` `a=v (dv)/(dx)`

`:.` `int_(v_1)^(v_2)vdv=int_(x_1)^(x_2)adx`