Question

A particle is moving in x-y-plane at 2 m/s along x-axis, 2 seconds later, its velocity is 4 m/s in a direction making 60° with positive x-axis. Its average acceleration for this period of motion is:

• A. √5 m/s², along y-axis
• B. √3 m/s², along y-axis
• C. √5 m/s², along at 60° with positive x-axis
• D. 3m/s², at 60° with positive x-axis.

Answer 1

Answer: (B)

√3 m/s², along y-axis

Answer 2

• Initial velocity: The particle moves along the x-axis at 2 m/s. $\vec{v_1} = 2 \hat{i}$ m/s

• Final velocity: After 2 seconds, its velocity is 4 m/s in a direction making 60° with the positive x-axis. $\vec{v_2} = (4 \cos 60^\circ) \hat{i} + (4 \sin 60^\circ) \hat{j}$ $\vec{v_2} = (4 \times \frac{1}{2}) \hat{i} + (4 \times \frac{\sqrt{3}}{2}) \hat{j}$ $\vec{v_2} = 2 \hat{i} + 2\sqrt{3} \hat{j}$ m/s

• Time interval: $\Delta t = 2$ s

• Average acceleration: $\vec{a}_{avg} = \frac{\Delta \vec{v}}{\Delta t} = \frac{\vec{v_2} - \vec{v_1}}{\Delta t}$ $\vec{a}_{avg} = \frac{(2 \hat{i} + 2\sqrt{3} \hat{j}) - (2 \hat{i})}{2}$ $\vec{a}_{avg} = \frac{2\sqrt{3} \hat{j}}{2}$ $\vec{a}_{avg} = \sqrt{3} \hat{j}$ m/s²

• Magnitude: $|\vec{a}_{avg}| = \sqrt{3}$ m/s²

• Direction: Along the y-axis.