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Given \( \vec{u} = 3\hat{i} + 4\hat{j} \) and \( \vec{a} = 0.4\hat{i} + 0.3\hat{j} \), find the net final velocity of the particle after 10 seconds.

1. \( 7 \, \text{units} \)
2. \( 8 \, \text{units} \)
3. \( 9 \, \text{units} \)
4. \( 10 \, \text{units} \)

Correct answer: \( 8 \, \text{units} \)

Solution

The final velocity is given by \( \vec{v} = \vec{u} + \vec{a}t \). Substituting \( \vec{u} = 3\hat{i} + 4\hat{j} \), \( \vec{a} = 0.4\hat{i} + 0.3\hat{j} \), and \( t = 10 \), we get \( \vec{v} = (3 + 0.4 \times 10)\hat{i} + (4 + 0.3 \times 10)\hat{j} = 7\hat{i} + 7\hat{j} \). The magnitude is \( \sqrt{7^2 + 7^2} = 7\sqrt{2} \approx 9.9 \approx 10 \).

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