question_answer

A particle is moving, eastwards with a velocity of 5 m/s. In 10 s, its velocity changes to 5 m/s northwards. The average acceleration in this time is:

A)  zero

B)  \[\frac{1}{\sqrt{2}}m/{{s}^{2}}\]towards north-west

C)  \[\frac{1}{\sqrt{2}}m/{{s}^{2}}\]towards north-east

D) \[\frac{1}{2}m/{{s}^{2}}\]towards north-west

E)  \[\frac{1}{2}m/{{s}^{2}}\]towards north

Correct Answer: B

Solution :

Average acceleration \[=\frac{\Delta \overrightarrow{v}}{\Delta t}\] \[\Delta v=\sqrt{v_{1}^{2}+v_{2}^{2}}=\sqrt{{{5}^{2}}+{{5}^{2}}}=5\sqrt{2}\] \[\therefore \]Average acceleration \[=\frac{5\sqrt{2}}{10}=\frac{1}{\sqrt{2}}m/{{s}^{2}}\]. towards north-west.