Question

A particle has an initial velocity of $3\hat{i}+4\hat{j}$ and an acceleration of $0.4\hat{i}+0.3\hat{j}$. Its speed 10s is?

• A. 7 units
• B. 8.5 units
• C. 10 units
• D. $7\sqrt{2}$ units

Answer 1

Answer: (D)

$7\sqrt{2}$ units

Answer 2

The initial velocity is $\vec{v_0} = 3\hat{i}+4\hat{j}$.

The acceleration is $\vec{a} = 0.4\hat{i}+0.3\hat{j}$.

The time is $t = 10$ s.

The final velocity $\vec{v}$ after time $t$ can be found using the equation of motion: $\vec{v} = \vec{v_0} + \vec{a}t$

Substitute the given values: $\vec{v} = (3\hat{i}+4\hat{j}) + (0.4\hat{i}+0.3\hat{j})(10)$ $\vec{v} = (3\hat{i}+4\hat{j}) + (4\hat{i}+3\hat{j})$ $\vec{v} = (3+4)\hat{i} + (4+3)\hat{j}$ $\vec{v} = 7\hat{i} + 7\hat{j}$

The speed is the magnitude of the final velocity vector: $\text{Speed} = |\vec{v}| = \sqrt{7^2 + 7^2}$ $\text{Speed} = \sqrt{49 + 49}$ $\text{Speed} = \sqrt{98}$ $\text{Speed} = \sqrt{49 \times 2}$ $\text{Speed} = 7\sqrt{2} \text{ units}$