Initial velocity of a particle is (3i + 4j) and acceleration is (0.4i + 0.3j). Its speed after 10 s will be:

Question

Initial velocity of a particle is \((3\hat{i} + 4\hat{j})\) and acceleration is \((0.4\hat{i} + 0.3\hat{j}).\) Its speed after 10 s will be:

(a) \(7\sqrt{2}\)

(b) 7 units

(c) 8.5 unit

(d) 10 unit

Answer 1

Correct option is : (a) \(7\sqrt{2}\)

\(\because\ \vec v = \vec u + \vec at\)

\(\therefore \ \vec v = (3\hat{i} + 4\hat{j}) + (0.4\hat{i} + 0.3\hat{j})\times10\)

\( = 3\hat{i}+ 4\hat{j} +4\hat{i} + 3\hat{j}\) 

or \(\vec v = 7\hat{i} + 7\hat{j}\therefore|\vec v| = \sqrt{7^2 + 7^2} = 7\sqrt{2}\)

Thus option (a) is correct.