Question

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

• A. Zero
• B. $\frac{1}{\sqrt{2}}\text{m/}\text{s}^{2}$toward north-west
• C. $\frac{1}{\sqrt{2}}\text{m/}\text{s}^{2}$toward north-east
• D. $\frac{1}{2}\text{m/}\text{s}^{2}$toward north-west

Answer 1

Answer: (B)

$\frac{1}{\sqrt{2}}\text{m/}\text{s}^{2}$toward north-west

Answer 2

$\Delta\overrightarrow{\upsilon} = {\overrightarrow{\upsilon}}_{2} - {\overrightarrow{\upsilon}}_{1}$

$\Delta\upsilon = \sqrt{\upsilon_{1}^{2} + \upsilon_{2}^{2} - 2\upsilon_{1}\upsilon_{2}\cos 90^{o}} = \sqrt{5^{2} + 5^{2}} = 5\sqrt{2}\Delta\upsilon = 5\sqrt{2}$

Average acceleration $= \frac{\Delta\upsilon}{\Delta t} = \frac{5\sqrt{2}}{10} = \frac{1}{\sqrt{2}}\text{m/}\text{s}^{2}$

toward north-west (As clear from the figure).