Question:medium
A block of mass \(2\,\text{kg}\), moving along the \(X\)-axis on a horizontal surface with a speed of \(4\,\text{ms}^{-1}\), enters a rough surface from \(x=0.5\,\text{m}\) to \(x=1.5\,\text{m}\). The retarding force on this rough surface is
\[
F=-12x\ \text{N}.
\]
The speed of the block as it just crosses the rough surface is
A block of mass \(2\,\text{kg}\), moving along the \(X\)-axis on a horizontal surface with a speed of \(4\,\text{ms}^{-1}\), enters a rough surface from \(x=0.5\,\text{m}\) to \(x=1.5\,\text{m}\). The retarding force on this rough surface is
\[
F=-12x\ \text{N}.
\]
The speed of the block as it just crosses the rough surface is
Show Hint
For a variable force, work is calculated using
\[
W=\int F\,dx.
\]
Then use the Work-Energy Theorem
\[
W=\Delta K
\]
to find the final speed directly without calculating acceleration.
Updated On: Jul 29, 2026
- Zero
- \(1.5\,\text{ms}^{-1}\)
- \(2\,\text{ms}^{-1}\)
- \(2.5\,\text{ms}^{-1}\)
Show Solution
The Correct Option is C
Solution and Explanation
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