---
title: "A block of mass \\(m\\) is sliding on a horizontal frictionless surface. In Trial 1, the block has an initial speed \\(v_1\\) and a constant horizontal force \\(F\\) is applied in the direction of motion for a fixed time interval \\(\\Delta t\\). In Trial 2, the block has an initial speed \\(v_2\\) (where \\(v_2 > v_1\\)) and the same force \\(F\\) is applied in the direction of motion for the same time interval \\(\\Delta t\\). Which of the following correctly compares the change in kinetic energy \\(\\Delta K\\) of the block for the two trials?"
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url: "https://nerd-notes.com/ubq/111552/"
date_modified: "2026-04-12T03:11:36+00:00"
---

# A block of mass \(m\) is sliding on a horizontal frictionless surface. In Trial 1, the block has an initial speed \(v_1\) and a constant horizontal force \(F\) is applied in the direction of motion for a fixed time interval \(\Delta t\). In Trial 2, the block has an initial speed \(v_2\) (where \(v_2 > v_1\)) and the same force \(F\) is applied in the direction of motion for the same time interval \(\Delta t\). Which of the following correctly compares the change in kinetic energy \(\Delta K\) of the block for the two trials?

A block of mass \(m\) is sliding on a horizontal frictionless surface. In Trial 1, the block has an initial speed \(v_1\) and a constant horizontal force \(F\) is applied in the direction of motion for a fixed time interval \(\Delta t\). In Trial 2, the block has an initial speed \(v_2\) (where \(v_2 > v_1\)) and the same force \(F\) is applied in the direction of motion for the same time interval \(\Delta t\). Which of the following correctly compares the change in kinetic energy \(\Delta K\) of the block for the two trials?

![A rectangular block of mass m rests on a flat horizontal line. A vector arrow labeled F points to the right from the right side of the block. A smaller arrow labeled v points to the right above the block to indicate its initial velocity.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1775963495-z3ukSP.jpg)

- **A.** \(\Delta K\) is the same for both trials because the same force is applied for the same time interval, delivering the same impulse to the block.
- **B.** \(\Delta K\) is the same for both trials because the block's change in velocity, \(\Delta v = \dfrac{F \Delta t}{m}\), is the same for both trials.
- **C.** \(\Delta K\) is greater in Trial 2 than in Trial 1 because the block travels a greater distance while the force is applied, resulting in more work being done on the block.
- **D.** \(\Delta K\) is greater in Trial 2 than in Trial 1 because the average power delivered to the block by the force \(F\) is smaller when the block is moving at a higher speed.

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/111552/*