A particle has an initial velocity of $(3 \hat{i}+4 \hat{j}) \mathrm{~m} / \mathrm{s}$ and a constan

Question

A particle has an initial velocity of $(3 \hat{i}+4 \hat{j}) \mathrm{~m} / \mathrm{s}$ and a constant acceleration of $(0.4 \hat{i}+0.3 \hat{j}) \mathrm{~m} / \mathrm{s}^{2}$. The magnitude of its velocity after 10 seconds will be

Professor PC Thomas Classes · Answer

(a) : $\vec{v} = \vec{u} + \vec{a}t = (3\hat{i}+4\hat{j}) + (0.4\hat{i}+0.3\hat{j})10 = 3\hat{i}+4\hat{j} + 4\hat{i}+3\hat{j} = 7\hat{i}+7\hat{j}$. \ Magnitude $|\vec{v}| = \sqrt{7^2+7^2} = 7\sqrt{2} \mathrm{~m} / \mathrm{s}$.