30. A particle has initial velocity ( 2 î + 3 ĵ ) and acceleration ( 0.3 î + 0.2 ĵ ). The magnitude of velocity after 10 seconds will be:

30. A particle has initial velocity ( 2 î + 3 ĵ ) and acceleration ( 0.3 î + 0.2 ĵ ). The magnitude of velocity after 10 seconds will be:

(a) 9√2 units

(b) 5√2 units

(c) 5 units

(d) 9 units

Answer :  (b) 5√2 units

The acceleration is constant.

\( \vec{v} = \vec{u} + \vec{a}t \)

\( = (2\hat{i} + 3\hat{j}) + (0.3\hat{i} + 0.2\hat{j})\,10 \)

\( = 5\hat{i} + 5\hat{j} \)

\( |\vec{v}| = \sqrt{5^2 + 5^2} \)

\( = 5\sqrt{2} \) units