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Step-by-Step Solution
Step 1: Identify the given quantities
• Mass of the box, m = 2 \text{ kg}
• Applied force, \overrightarrow{F} = (20\,\hat{i} + 10\,\hat{j}) \text{ N}
• Initial velocity of the box, u = 0 (at rest)
• Time, t = 10 \text{ s}
Step 2: Calculate the acceleration of the box
From Newton’s second law, \overrightarrow{F} = m\,\overrightarrow{a} . Thus,
\overrightarrow{a}
= \frac{\overrightarrow{F}}{m}
= \frac{20\,\hat{i} + 10\,\hat{j}}{2}
= 10\,\hat{i} + 5\,\hat{j}.
Step 3: Write the formula for displacement under constant acceleration
Since the box starts from rest, its displacement vector after time t is
\overrightarrow{s} = \frac{1}{2} \,\overrightarrow{a}\,t^2.
Step 4: Substitute the values to find the displacement vector
\overrightarrow{s}
= \frac{1}{2}\,(10\,\hat{i} + 5\,\hat{j})\,\times (10)^2
= \frac{1}{2}\,(10\,\hat{i} + 5\,\hat{j}) \times 100.
Simplifying,
\overrightarrow{s}
= 50\,(10\,\hat{i} + 5\,\hat{j})
= (500\,\hat{i} + 250\,\hat{j}) \text{ m}.
Step 5: Extract the displacement along the x-axis
The displacement along the x-axis (the \hat{i} direction) is the x-component of
\overrightarrow{s} , which is 500 \text{ m} .
Final Answer:
The displacement along the x-axis after 10 s is 500 m.
