27. A particle has initial velocity ( 3 î + 4 ĵ ) and has acceleration ( 0.4 î +0.3 ĵ ). It’s speed after 10 s is:
(a) 7 units
(b) 7√2 units
(c) 8.5 units
(d) 10 units
Answer : (b) 7√2 units
\( \vec{v} = \vec{u} + \vec{a}t \)
\( = (3\hat{i} + 4\hat{j}) + (0.4\hat{i} + 0.3\hat{j})\,10 \)
\( = 3\hat{i} + 4\hat{j} + 4\hat{i} + 3\hat{j} \)
\( = 7\hat{i} + 7\hat{j} \)
\( |\vec{v}| = \sqrt{7^2 + 7^2} \)
\( = \sqrt{7^2(1+1)} \)
\( = 7\sqrt{2} \) units
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