question_answer

A body is moving with velocity 30 m/s towards east. After 10 s its velocity becomes 40 m/s towards north. The average acceleration of the body is

A) \[7\text{ }m/{{s}^{2}}\]                      

B) \[\sqrt{7}\text{ }m/{{s}^{2}}\]

C) \[5\text{ }m/{{s}^{2}}\]                      

D) \[1\text{ }m/{{s}^{2}}\]

Correct Answer: C

Solution :

\[Average\,\,acceleration\,\,=\,\,\frac{Change\,\,in\,\,velocity}{Total\,\,time}\] \[\overrightarrow{{{\nu }_{L}}}=\,\,30\hat{i}\,\,m/s\,\,and\,\,{{\vec{v}}_{i}}=40\hat{j}m/s\] \[\left| \Delta \vec{\nu } \right|=\sqrt{{{30}^{2}}+{{40}^{2}}}=\,\sqrt{900+1600}\,\,=\,\,50\,m/s\] \[\vec{a}=\frac{\left| {{{\vec{V}}}_{f}}-{{{\vec{V}}}_{i}} \right|}{\Delta t}\,\,=\,\,\frac{50}{10}\,\,=\,\,5\,m{{s}^{-2}}\]