question_answer 45)

                  Following are four different relations about displacement, velocity and acceleration for the motion of a particle in general. Choose the incorrect one (s)                 (a) \[{{\upsilon }_{av}}=\,\frac{1}{2}\,[\upsilon \,({{t}_{1}})\,+\,\upsilon \,({{t}_{2}})]\]                 (b) \[{{\upsilon }_{av}}=\,\frac{r\,({{t}_{2}})-\,r({{t}_{1}})}{{{t}_{2}}-{{t}_{1}}}\]                 (c) \[{{v}_{a\upsilon }}=\frac{1}{2}(v({{t}_{2}})-v({{t}_{1}})({{t}_{2}}-{{t}_{1}})\]                 (d) \[{{a}_{a\upsilon }}=\,\frac{\nu \,({{t}_{2}})\,-\,\nu \,({{t}_{1}})}{{{t}_{2}}-{{t}_{1}}}\]

Answer:

                  (a, c) (a) is true only if acceleration is constant (c) is also not correct as \[\vec{v}\,({{t}_{2}})\,-\nu ({{t}_{1}})\]                 \[=\,{{\vec{a}}_{a\upsilon }}({{t}_{2}}-\,{{t}_{1}})\]