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

See figure. Here, we have v_i =5iand v_f =5i

Change in velocity $={\mathrm{v}}_{\mathrm{f}}-{\mathrm{v}}_{\mathrm{i}}=5\mathrm{j}-5\mathrm{i}$
The magnitude of change of velocity
$=\left|{\mathbf{v}}_{\mathrm{f}}-{\mathbf{v}}_{\mathrm{i}}\right|=\sqrt{\left[(5{)}^2+(5{)}^2\right]}=5\sqrt{2}\mathrm{m}/\mathrm{s}$
$\therefore$ Average acceleration
${\mathrm{a}}_{\mathrm{av}}=\frac{\mathrm{change} \mathrm{in} \mathrm{velocity}}{\mathrm{time} \mathrm{taken}}=\frac{5\sqrt{2}}{10}=\frac{1}{\sqrt{2}}\mathrm{m}/{\mathrm{s}}^2$