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A particle has initial velocity $(3\hat{i} + 4\hat{j})$ and has acceleration $(0.4\hat{i} + 0.3\hat{j})$. Its speed after 10 s is
A
10 units
B
7 units
C
$7\sqrt{2}$ units
D
8.5 units
Detailed Solution
$\vec{v} = \vec{u} + \vec{a}t$
$\vec{v} = (3\hat{i} + 4\hat{j}) + (0.4\hat{i} + 0.3\hat{j})\times10$
$\vec{v} = (3 + 4)\hat{i} + (4 + 3)\hat{j} = 7\hat{i} + 7\hat{j}$
Speed $= |\vec{v}| = \sqrt{7^2 + 7^2} = \sqrt{98}$
$= 7\sqrt{2}$ units
$\vec{v} = (3\hat{i} + 4\hat{j}) + (0.4\hat{i} + 0.3\hat{j})\times10$
$\vec{v} = (3 + 4)\hat{i} + (4 + 3)\hat{j} = 7\hat{i} + 7\hat{j}$
Speed $= |\vec{v}| = \sqrt{7^2 + 7^2} = \sqrt{98}$
$= 7\sqrt{2}$ units